Exhibit 10.8

EXECUTION VERSION

GULF OF MEXICO PROGRAM

MANAGEMENT

AND

AMI AGREEMENT

by and between

COBALT INTERNATIONAL ENERGY, L.P.,

a Delaware Limited Partnership

and

TOTAL E&P USA, INC.,

a Delaware corporation

INDEX

ii

EXHIBITS

iii

GULF OF MEXICO PROGRAM

MANAGEMENT AND AMI AGREEMENT

This Gulf of Mexico Program Management and AMI Agreement (the “Agreement”) is entered into by and between Cobalt International Energy, L.P., a Delaware limited partnership (“Cobalt”), and TOTAL E&P USA, INC., a Delaware corporation (“Total”) on 6th April, 2009 (the “Effective Date”). Cobalt and Total are each referred to in this Agreement individually as a “Party” and, together, as the “Parties.”

RECITALS

A.                                   On even date herewith, Cobalt and Total have entered into a Simultaneous Exchange Agreement (the “Exchange Agreement”) and two Purchase and Sale Agreements (the “PSAs”), as a result of which the Parties shall, subject to required governmental approvals, on the Effective Date jointly own interests in certain offshore federal leases located in the Gulf of Mexico; and

B.                                     Cobalt and Total desire to participate in the GoM Program (defined below) and to establish the AMI (as defined below), all in the manner described in this Agreement and subject to the provisions hereof.

Therefore, in consideration of the premises and the respective agreements contained in this Agreement, the benefits to be derived by each Party hereto and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties agree as follows:

ARTICLE 1. DEFINITIONS

1.1                                 Definitions.

Unless provided otherwise in this Agreement, each capitalized term in this Agreement has the meaning given to it in this Article.

1.1.1                        “Acquired Interest” has the meaning specified in Section 5.1.2.

1.1.2                        “Acquiring Party” has the meaning specified in Section 5.1.2.

1.1.3                        “Acquisition Cost” has the meaning specified in Section 5.1.5.

1.1.4                        “Administrative Costs” means all of the following costs incurred by Cobalt in managing the GoM Program: (i) salaries, wages and related costs, including benefits and travel for personnel (excluding the salary, benefits and other costs of Secondees), (ii) lease and maintenance costs related to office facilities, (iii) legal, accounting and other services and (iv) all other direct costs of an administrative nature.

1.1.5                        “Affiliate” means any Person that:

(a)                                       is owned or controlled by a Party;

(b)                                      is owned or controlled by any other Person that is owned or controlled by a Party;

(c)                                       owns or controls a Party; or

(d)                                      is owned or controlled by any Person that owns or controls a Party.

For the purposes of this definition, ownership or control means (i) the ownership or control, directly or indirectly, of fifty percent (50%) or more of the shares, voting rights, or interest (or similar rights to direct the management and policies of) in any Person and (ii) the general partner in any limited partnership. Notwithstanding the foregoing, no private equity fund or its affiliate will be deemed to be an “Affiliate” as long as such private equity fund is not a private equity fund (x) controlled by a Person whose primary business is oil and gas operations or (y) qualified by the Minerals Management Service to hold oil and gas leases in the Gulf of Mexico. For the avoidance of doubt, as of the Effective Date, none of the current limited partners of Cobalt are controlled by a Person whose primary business is oil and gas operations.

1.1.6                        “Agreement” has the meaning specified in the opening paragraph of this Agreement.

1.1.7                        “Agreement Term” has the meaning specified in Section 7.1.

1.1.8                        “AMI” has the meaning specified in Section 5.1.1.

1.1.9                        “AMI Share” means an undivided sixty percent (60%) as to Cobalt and an undivided forty percent (40%) as to Total.

1.1.10                  “AMI Term” has the meaning specified in Section 5.1.1.

1.1.11                  “Authorization for Expenditure” or “AFE” has the meaning provided in the applicable Operating Agreement.

1.1.12                  “BHP Block” means Green Canyon Block 187.

1.1.13                  “BHP Interest” means 50% of all of the oil and gas leasehold interests held by Cobalt or any of its Affiliates as of the Effective Date with respect to the Lease covering the BHP Block.

2

1.1.14                  “business day” means a day other than a Saturday, a Sunday, a federal holiday or a day on which commercial banks in the jurisdiction of receipt are authorized by law to close.

1.1.15                  “Change of Control Election” has the meaning specified in Section 7.3.

1.1.16                  “Cobalt” has the meaning specified in the opening paragraph of this Agreement.

1.1.17                  “Cobalt Non-GoM Program Blocks” means (i) Walker Ridge Blocks 8, 51 and 52 (the Shenandoah prospect) and Green Canyon Blocks 816, 859, 860 and 903 (the Heidelberg prospect) and (ii) any blocks in which an Acquired Interest was offered by Cobalt to Total and which Total did not elect or was deemed not to elect to acquire in accordance with Article 5 hereof.

1.1.18                  “Combined Operations Council” has the meaning specified in Section 2.3.

1.1.19                  “Combined Operations Team” has the meaning specified in Section 2.2.

1.1.20                  “Confidential Work Product” means all proprietary geophysical, geochemical, drilling, engineering or other similar technical data, along with information, reports, studies, analysis, models or similar data and documents that are produced, acquired or developed by the Parties during the Agreement Term as part of the GoM Program.

1.1.21                  “Effective Date” has the meaning specified in the opening paragraph of this Agreement.

1.1.22                  “Event of Default” has the meaning specified in Section 7.2.

1.1.23                  “Exchange Agreement” has the meaning specified in the first paragraph of the Recitals.

1.1.24                  “Existing Third Party AMIs” has the meaning specified in Section 5.1.11.

1.1.25                  “Form JOA” means a joint operating agreement in the same form as the operating agreement attached hereto as Exhibit A.

1.1.26                  “GoM Program” means all activities related generally to the Joint Participation Area (excluding any blocks with respect to which oil and gas leasehold interests have been acquired by preferential purchase right holders in connection with either of the PSAs) and all Joint Leases during the Agreement Term.

1.1.27                  “GoM Program Costs” has the meaning specified in Section 3.1.2.

1.1.28                  “include” and “including” mean without limitation.

3

1.1.29                  “Initial Admin Cost Estimate” has the meaning specified in Section 3.1.2(a).

1.1.30                  “Joint Leases” means any Lease in which both Cobalt and Total own an undivided interest, as of or after the Effective Date.

1.1.31                  “Joint Participation Area” means all federal blocks within the entire Outer Continental Shelf of the Gulf of Mexico other than (i) the Cobalt Non-GoM Program Blocks and (ii) the Total Non-GoM Program Blocks.

1.1.32                  “Large Development” means a development that will require the Parties to design, construct and own a permanently anchored host facility to collect and transport oil or natural gas from such development.

1.1.33                  “Lease” means any Outer Continental Shelf of the Gulf of Mexico federal oil and gas lease (or portion thereof).

1.1.34                  “Non-Acquiring Party” has the meaning specified in Section 5.1.2.

1.1.35                  “Non-OA/Administrative GoM Expenses” means all costs of a third party service provider incurred by Cobalt after the Effective Date in managing the GoM Program, including information technology support costs, including workstations, software, software licenses, networks, data storage, data handling and other communication services, but excluding Administrative Costs and any costs charged under an Operating Agreement.

1.1.36                  “Obligation Well” has the meaning given such term in the Exchange Agreement.

1.1.37                  “Obligation Well Program” has the meaning given such term in the Exchange Agreement.

1.1.38                  “Obligation Well Program Term” has the meaning given such term in the Exchange Agreement.

1.1.39                  “Operating Agreement” means the applicable offshore operating agreement entered into by the Parties governing a Joint Lease, or, if applicable, any Third Party Operating Agreement.

1.1.40                  “Party” has the meaning specified in the opening paragraph of this Agreement.

1.1.41                  “Person” means any individual, corporation, limited liability company, partnership, limited partnership, trust, association, or other entity.

1.1.42                  “PSAs” has the meaning specified in the first paragraph of the Recitals.

4

1.1.43                  “Secondees” means any person seconded to Cobalt pursuant to the Secondment Agreement.

1.1.44                  “Secondment Agreement” has the meaning specified in Section 4.1.5.

1.1.45                  “Sonangol Blocks” means those blocks depicted on Exhibit G to the Exchange Agreement as the “Sonangol Blocks.”

1.1.46                  “Sonangol Interest” means 25% of all of the oil and gas leasehold interests held by Cobalt or any of its Affiliates as of the Effective Date with respect to the Leases covering the Sonangol Blocks.

1.1.47                  “Specified Change of Control” has the meaning specified in Section 7.3.

1.1.48                  “Tag-Along Notice” has the meaning specified in Section 6.2.1.

1.1.49                  “Tag-Along Right” has the meaning specified in Section 6.2.1.

1.1.50                  “Tag Along Share” means that Party’s working interest divided by the sum of the Parties’ working interest determined on the date of the Tag Along Notice, expressed as a percentage.

1.1.51                  “Tag-Along Transferee” has the meaning specified in Section 6.2.1.

1.1.52                  “Tag Offeree” has the meaning specified in Section 6.2.1.

1.1.53                  “Tariff’ has the meaning specified in Section 4.1.6.

1.1.54                  “Third Party Operating Agreement” means any operating agreement with any third party to which any oil and gas leasehold interest that is attributable to a Lease owned by a Party is subject or which a Party is obligated to enter into or negotiate pursuant to the terms of an agreement to which a Party is subject as of the Effective Date.

1.1.55                  “Total” has the meaning specified in the opening paragraph of this Agreement.

1.1.56                  “Total Non-GoM Program Blocks” means (i) the blocks listed on Exhibit F to the Exchange Agreement, and (ii) any blocks in which an Acquired Interest was offered by Total to Cobalt and which Cobalt did not elect or was deemed not to elect to acquire in accordance with Article 5 hereof.

1.1.57                  “Transfer” has the meaning specified in Section 6.1.1.

1.1.58                  “Transferor” has the meaning specified in Section 6.2.1.

1.1.59                  “Well Costs” has the meaning given such term in the Exchange Agreement.

5

1.1.60                  “Work Program and Budget” has the meaning specified in Section 3.2.

ARTICLE 2. GoM PROGRAM

2.1                                 GoM Program.

In accordance with the terms of this Agreement, the Parties shall work in good faith with each other as follows with respect to the GoM Program:

2.2                                 Combined Operations Team.

Cobalt and Total shall designate a team of Cobalt employees and Secondees (the “Combined Operations Team”) necessary to perform the day-to-day activities associated with the GoM Program and to make recommendations to the Combined Operations Council (defined below) regarding the GoM Program. The Parties shall determine the number and skills of the participants on the Combined Operations Team. The Combined Operations Team shall be under the direct supervision of Cobalt, but shall neither have any authority to make any decisions with respect to the GoM Program nor shall it be delegated any authority from Cobalt, Total or the Combined Operations Council outside of the Combined Operations Team members’ responsibilities as an employee of Cobalt or as a Secondee. Subject to applicable confidentiality restrictions and applicable law, members of the Combined Operations Team shall provide information to one another regarding the GoM Program in order to make its recommendations to the Combined Operations Council.

2.3                                 Combined Operations Council.

Cobalt and Total shall designate a council (the “Combined Operations Council”) comprised of a small group of executives made up of Cobalt employees and Total employees (Secondees or non-Secondees) to develop short, medium and long term objectives for and evaluate the results of the GoM Program. The Combined Operations Council shall be a non-decision making body that will rely on input from the Combined Operations Team, Cobalt and Total, as appropriate. As such, no action taken by the Combined Operations Council shall be binding upon the Parties. It is anticipated that Total would have three (3) representatives on the Combined Operations Council and Cobalt would have a sufficient number of representatives on the Combined Operations Council to provide for the discussion and exchange of information relating to the GoM Program that would enable each Party to make informed decisions regarding the GoM Program. Each Party is entitled to invite any of its employees to a specific Combined Operations Council meeting where such employee’s expertise would provide valuable input to any matters discussed or proposed to be discussed by the Combined Operations Council. Subject to applicable law, the Combined Operations Council shall consider the following matters regarding the GoM Program: strategy adherence, staffing, competition in the Gulf of Mexico, the external environment, technology application and advances, non-decisional input on the current and future year plans, well results, operational

6

activities and developmental planning. The Combined Operations Council shall meet monthly in Cobalt’s Houston office and on an ad hoc basis as necessary as called for by either Cobalt or Total. The members of the Combined Operations Council may attend any meeting in person or by telephone. The Combined Operations Council shall hear and review the recommendations of the Combined Operations Team and any other issues raised by Cobalt or Total. Members of the Combined Operations Team and other technical experts of either Party shall participate in meetings of the Combined Operations Council as appropriate. The Combined Operations Council shall have a Cobalt designated Chairman and Secretary. The Chairman shall report solely to Cobalt’s Chief Executive Officer. The Secretary shall develop meeting agendas and record minutes of the meetings.

2.4                                 Meetings of Principals.

In addition to the meetings of the Combined Operations Council, Cobalt’s Chief Executive Officer and/or members of Cobalt’s executive management and members of Total’s executive management shall meet at least semi-annually to consider strategy for and results of the GoM Program.

2.5                                 Joint Data.

Subject to Section 3.2, the Parties shall own all technical or scientific information developed or acquired by Cobalt and/or Total in the course of the GoM Program (including know-how, confidential information, trade secrets, computer programs, utility models, patents, inventions, copyrights, rights in design (whether registered or unregistered) and any other intellectual property rights) in the same proportion to which each Party paid for such technical or scientific information, except to the extent such information is jointly owned under an Operating Agreement, or except to the extent such information is subject to other third party restrictions. To the extent Cobalt acquires a base license for data after the Effective Date, Cobalt shall use commercially reasonable efforts to acquire, on behalf of the Parties, joint rights to use the data covered by such license.

2.6                                 Operatorship.

Cobalt shall be designated as operator for all exploratory and appraisal operations. Upon completion of appraisal operations (as defined under the relevant Operating Agreement), operatorship shall be determined by the Parties with the greatest importance being placed on majority (or largest) working interest ownership and the respective experience of Large Developments.

7

ARTICLE 3. GoM PROGRAM COST SHARING

3.1                                 GoM Program Costs.

3.1.1                        Total agrees to pay Cobalt an amount equal to forty percent (40%) of all of the GoM Program Costs.

3.1.2                        For the purposes of this Agreement, the “GoM Program Costs” shall be, for costs incurred from the Effective Date through the termination date of this Agreement:

(a)                                  $21,300,000 per year, which approximates the Parties’ initial estimate of the annual Administrative Costs as of the Effective Date (“Initial Admin Cost Estimate”), as adjusted pursuant to Section 3.1.3 and to be reduced during each year by any amounts charged as overhead under any applicable Operating Agreement; plus

(b)                                 Subject to Total’s right to elect not to participate under Section 3.2, Non-OA/Administrative GoM Expenses directly incurred in conducting the GoM Program.

3.1.3                        The dollar amount to be paid pursuant to Section 3.1.2(a) for Administrative Costs shall be prorated for the first calendar year of this Agreement, and the Initial Admin Cost Estimate shall be adjusted every two (2) years to reflect any trend in historic and anticipated costs, with the first such adjustment taking place two (2) years after the Effective Date.

3.1.4                        The GoM Program Costs shall not include any amounts for which Total has been charged by Cobalt under an Operating Agreement. This Agreement does not limit or reduce the amounts payable by Total under the applicable Operating Agreement.

3.2                                 Annual Program and Budget.

For information purposes, the estimated program and budget for the GoM Program for the remainder of the 2009 calendar year is as set out in Exhibit B. After discussion at the Combined Operations Council and on or before the first day of September of each calendar year, Cobalt shall deliver to Total, a proposed budget for the following calendar year outlining the GoM Program’s forecasts of the Administrative Costs, the Non-OA/Administrative GoM Expenses and, to the extent then developed, a work program and budget of Well Costs to be included on AFEs (the “Work Program and Budget”). Within twenty (20) days of such delivery, the Combined Operations Council shall meet to review and discuss the Work Program and Budget, and within thirty (30) days after such meeting, Total shall notify Cobalt as to any line item cost on the Work Program and Budget relating to Non-OA/Administrative GoM Expenses in which Total elects not to participate. If Total does not agree to participate in any Non-OA/Administrative GoM Expenses, then Total shall not be entitled to the benefits of such Non-OA/Administrative GoM Expenses to which it elected not to participate and shall not have ownership rights or access to any technical or scientific information developed, acquired or produced as a result of the incurrence by Cobalt of such Non-OA/Administrative GoM Expenses. On

8

or before the first day of July of each year, Cobalt shall deliver to the Combined Operations Council a progress report comparing and reconciling the Work Program and Budget to actual costs and activities. In addition, Cobalt shall promptly notify Total if any line item on the Work Program and Budget is exceeded by more than ten percent (10%). The Work Program and Budget shall not require the approval of either Party, but, subject to the Exchange Agreement, each Party shall retain its rights under the applicable Operating Agreement to elect whether or not to participate in such work.

3.3                                 Payment.

Cobalt shall bill Total on or before the last day of each month for Total’s proportionate share of the GoM Program Costs for the preceding month. Such bills shall be accompanied by statements identifying credits and expenditures in the same categories as the Work Program and Budget so that the actual monthly expenditure can be compared against the budgeted monthly expenditure. Total shall pay Cobalt the amount set forth in each such bill within fifteen (15) business days after receipt of such bill.

ARTICLE 4. SECONDMENTS

4.1                                 Secondments.

4.1.1                        The Parties shall diligently and in good faith undertake the following secondment process.

4.1.2                        Cobalt shall offer secondment positions for experienced Total personnel in senior technical positions in areas such as geosciences, drilling and engineering in support of the GoM Program to be located in Cobalt’s offices in Houston. The number of secondment positions offered at any one time shall not be less than eight (8). Cobalt shall provide Total, for each secondment, the following information:

(a)                                  The job level, job description, scope of responsibility and deliverables; and

(b)                                 The duration of the secondment.

4.1.3                        Total shall nominate Total personnel that it considers reasonably qualified to fulfill the designated purpose and scope of such secondment(s). Cobalt shall evaluate each such proposed secondee by considering (i) the expertise and experience required for the position and the expertise and experience of the proposed personnel, and (ii) Cobalt’s view as to how such proposed personnel would work with Cobalt personnel as a team. Cobalt shall notify Total which, if any, nominated personnel are approved, which approval shall not be unreasonably withheld.

9

4.1.4                        All Secondees shall execute a confidentiality agreement agreeing to keep in the strictest confidence (i) to the same extent Cobalt employees are subject to a confidentiality obligation, any information covered by a data license or other agreement which so binds Cobalt, (ii) the Confidential Work Product and (iii) all proprietary confidential data of Cobalt. Any Cobalt employees that are provided Total proprietary confidential data or Confidential Work Product prepared by the Parties shall likewise sign a confidentiality agreement in favor of Total.

4.1.5                        Any secondment under this Agreement shall be in accordance with a secondment agreement to be negotiated by the Parties and entered into within thirty (30) days after the Effective Date (the “Secondment Agreement”).

4.1.6                        Pursuant to an agreed upon tariff (the “Tariff”):

(a)                                  The initial Tariff shall be $300,000 per Secondee, which approximates the Parties’ initial estimate of the annual costs related to secondments and Secondees, including the salary and benefits of such Secondees but excluding the cost of travel to expatriate to Houston, visas, moving expenses, housing allowances, tax equalization payments, currency adjustments, and any other foreign assignment costs/allowances. Business expenses of Secondees shall be paid by Cobalt in the same manner as Cobalt personnel.

(b)                                 The Tariff to be paid pursuant to this Section 4.1.6 shall be prorated for the first calendar quarter that any Secondee begins or exits his or her secondment.

(c)                                  The Tariff shall be adjusted every two (2) years to reflect any trend in historic and anticipated costs, with the first such adjustment taking place two (2) years from the Effective Date.

(d)                                 On or before the last day of each fiscal quarter, Total shall bill Cobalt for sixty percent (60%) of the Tariff and Cobalt shall pay Total the amount set forth in each such bill within fifteen (15) business days after receipt of such bill.

ARTICLE 5. AREA OF MUTUAL INTEREST

5.1                                 Area of Mutual Interest.

5.1.1                        The Parties hereby establish an area of mutual interest (“AMI”) which shall cover the Joint Participation Area. The term of the AMI shall be for a period commencing on the Effective Date and ending (a) on the tenth anniversary of the Effective Date, (b) the date of termination of this Article 5 in accordance with

10

Section 5.1.12 or (c) the date of termination of this Agreement, whichever is the earliest (“AMI Term”). This AMI shall replace all of the prior AMIs between the Parties listed on Exhibit C which are hereby terminated.

5.1.2                        During the AMI Term, if (other than through a joint bid with the other Party or its Affiliate) a Party or its Affiliate (the “Acquiring Party”) acquires any interest in an oil and/or gas lease in one or more blocks within the Joint Participation Area, whether by cash sale, property swap, or farm-in by which an interest may be earned or otherwise acquired by conducting drilling, seismic, or other operations, or otherwise (“Acquired Interest”), then the Acquiring Party shall notify the other Party (“Non-Acquiring Party”), in writing, within thirty (30) days of such acquisition. Notwithstanding the immediately preceding sentence, a sale or other disposition of equity in a Party or other change of control in a Party shall not be deemed to be such an acquisition.

5.1.3                        If a Party or its Affiliate seeks to acquire an Acquired Interest that would be subject to a preferential right to purchase upon a subsequent transfer to the other Party, the first Party will use commercially reasonable efforts to offer the other Party the opportunity to participate in the offer and to jointly acquire title to such Acquired Interest in proportion to each Party’s AMI Share.

5.1.4                        The Non-Acquiring Party shall then have the right and option, but not the obligation, for a period of thirty (30) days from the receipt of such notice, to elect to acquire its AMI Share of the Acquired Interest by providing written notice of its election to the Acquiring Party prior to the expiration of such thirty (30) day period. Failure of the Non-Acquiring Party to provide written notice to the Acquiring Party prior to the expiration of such time period shall be deemed an election by the Non-Acquiring Party not to acquire any interest in the Acquired Interest.

5.1.5                        The notice from the Acquiring Party provided for in Section 5.1.2 shall contain all information and copies of Leases (to the extent the Acquiring Party has such Leases in its possession), agreements by which the Acquired Interest may be acquired, and all other documents to be entered into with respect thereto. Such notice shall also state in reasonable detail the out-of-pocket cost and expense of such acquisition and the full consideration for such Acquired Interest (collectively, the “Acquisition Cost”). In the case of an acquisition of a package of oil and gas interests that includes interests outside the AMI, or if the proposed acquisition is structured as an exchange of property, the Acquired Interest shall be separately valued, and the notice provided for in Section 5.1.2 shall state the monetary value attributed to the Acquired Interest.

5.1.6                        If the Non-Acquiring Party properly makes an election to acquire its AMI Share of such Acquired Interest, the Acquiring Party shall, within thirty (30) days after

11

receipt of the Non-Acquiring Party’s election, assign to the Non-Acquiring Party the Non-Acquiring Party’s AMI Share of such Acquired Interest, free and clear of any and all burdens created by the Acquiring Party other than those burdens, if any, associated with the acquisition of such Acquired Interest.

5.1.7                        Contemporaneously with the receipt of the assignment referred to in Section 5.1.6, the Non-Acquiring Party shall promptly reimburse the Acquiring Party for and assume the Non-Acquiring Party’s AMI Share of all Acquisition Costs incurred in acquiring the Acquired Interest (which, in the case of a package or exchange transaction described in Section 5.1.5, shall be the monetary value attributed to the Acquired Interest plus a proportionate share of out-of-pocket costs and expenses of such acquisition).

5.1.8                        If the Non-Acquiring Party elects or is deemed to have elected not to acquire such Acquired Interest, the Acquiring Party shall have no further obligation to the Non-Acquiring Party under the terms of this Article 5 with respect to such Acquired Interest and such Acquired Interest shall not be subject to the terms of this Agreement and shall be deemed excluded from the provisions of this Agreement for all purposes.

5.1.9                        If the Non-Acquiring Party elects to acquire such Acquired Interest, such Acquired Interest will be a Joint Lease for the purposes of this Agreement and if such Joint Lease is not subject to an operating agreement, the Parties shall enter into an operating agreement in the form of the Form JOA.

5.1.10                  The provisions of this Article 5 shall not apply to:

(a)                                  the Cobalt Non-GoM Program Blocks or the Total Non-GoM Program Blocks; or

(b)                                 Acquired Interests acquired through a merger, corporate reorganization, consolidation, scheme of arrangement or other corporate transaction; or

(c)                                  Acquisitions of a package of oil and gas interests or exchanges of property that includes leasehold interests or other interests both within the AMI and outside of the AMI, where the leasehold interests or other interests within the AMI represent less than fifty percent (50%) of the consideration being paid by the Acquiring Party for such acquisition; or

(d)                                 Acquired Interests in respect of any block within an area for which material Non-OA/Administrative GoM Expenses were incurred in respect of such block or area by Cobalt and not Total due to Total’s election not to participate in such Non-OA/Administrative GoM Expenses, pursuant to Section 3.2; or

12

(e)                                  Acquired Interests in respect of any block within an area for which material expenses were incurred by Total to conduct activities in respect of such block or area after Total proposed in writing that Cobalt conduct such activities as part of the GoM Program and which activities Cobalt elected not to perform; or

(f)                                    Acquired Interests acquired in a property or like-kind exchange transaction where the Non-Acquiring Party did not elect to exercise its Tag-Along Right pursuant to Section 6.2.1;

(g)                                 Acquired Interests acquired by a Party or its Affiliate pursuant to any preferential right to purchase in an Operating Agreement; or

(h)                                 the initial acquisition of Acquired Interests in Walker Ridge Blocks 90 and 133 pursuant to the Minerals Management Service’s Central Gulf of Mexico Lease Sale 208.

5.1.11                  The application of this Article 5 is subject to the AMIs and offer-back obligations in respect of the leases listed in Exhibit D concerning a third party (“Existing Third Party AMIs”). Where an Acquired Interest is subject to this Article 5 and an Existing Third Party AMI, the Acquiring Party shall first offer the Acquired Interest to all relevant third parties under the Existing Third Party AMI before offering the Acquired Interest (or part thereof after the exercise of the rights under the Existing Third Party AMI) to the Non-Acquiring Party under this Article 5. Neither Party shall extend an Existing Third Party AMI without the written consent of the other Party.

5.1.12                  It is not the intention of the Parties to restrict the right of any Party or its Affiliate to submit a bid at any OCS lease sale as to any block offered at any OCS lease sale or otherwise acquire an interest in any blocks within the Joint Participation Area. Notwithstanding anything to the contrary in this Agreement, if at any time during the Agreement Term, more than one of the Parties or its Affiliates (i) are on the list of restricted joint bidders for OCS lease sales as issued by the Minerals Management Service pursuant to 30 CFR 256.41 (or under any successor regulations) or (ii) otherwise would have been qualified to be on the list described in clause (i) above based on the aggregate worldwide average daily production of such Party and its Affiliates for any six month period ending after the Effective Date (if such list were produced on the last day of such six month period with respect to such period), then this Article 5 (other than the confidentiality obligation under Section 5.1.13) shall immediately terminate and be of no further effect. Furthermore, if at anytime during the Agreement Term, the AMI together with any Existing Third Party AMI involves two or more companies described in clause (i) or (ii) above, then in such instance, an provision hereof that would cause bids at any lease sale to be disqualified under 30 CFR 256.44 shall be deemed not

13

to apply to the extent but only to the extent necessary to avoid such disqualification.

5.1.13                  If a Non-Acquiring Party elects not to participate in an acquisition of an Acquired Interest, the Non-Acquiring Party will nevertheless continue to be bound by the confidentiality obligations of this Agreement with respect to such Acquired Interest.

ARTICLE 6. TRANSFER OF INTEREST IN JOINT LEASES

6.1                                 Transfers of Interest.

6.1.1                        Neither Party may assign, transfer or convey by assignment, sale, farmout, exchange or otherwise (collectively, a “Transfer”) in whole or in part this Agreement or any of its oil and gas leasehold interests in any Joint Lease, except in accordance with this Article 6. Notwithstanding the immediately preceding sentence, a sale or other disposition of equity in a Party or other change of control in a Party shall not be deemed a Transfer.

6.1.2                        Any assignment permitted hereunder shall be subject to all of the terms and conditions of this Agreement and any applicable Operating Agreement.

6.1.3                        The foregoing notwithstanding, subject to Section 24.1.3 of the Form JOA and other similar maintenance of interest obligations in an Operating Agreement, either Party shall be entitled to Transfer an interest in this Agreement and its oil and gas leasehold interests in the Joint Leases to an Affiliate without the consent of the other Party, but the transferring Party shall remain liable for the performance of its obligations hereunder notwithstanding such transfer, and the Affiliate shall be bound by its transferor’s transfer restrictions hereunder. Notwithstanding the foregoing, if any transferee Affiliate ceases to be an Affiliate of the transferring Party within two (2) years of the Transfer to such Affiliate, then such transferred interest in this Agreement or the oil and gas leasehold interests in the Joint Leases shall be immediately reassigned to the original transferring Party before the transferee Affiliate ceases to be an Affiliate of the original transferring Party.

6.1.4                        Except for the oil and gas leasehold interests in the Joint Leases comprising prospects associated with wells in the Obligation Well Program, Cobalt shall have the right (subject to any transfer restrictions and preferential rights to purchase imposed by any applicable Operating Agreement) to freely Transfer any of its interests in the oil and gas leasehold interests in the Joint Leases. Cobalt shall have the right (subject to any transfer restrictions imposed by any applicable Operating Agreement) to freely Transfer any of its interests in the oil and gas leasehold interests in the Joint Leases comprising prospects associated with a well

14

in the Obligation Well Program after such applicable Obligation Well has been drilled.

6.1.5                        Until the second anniversary of the Effective Date, Total shall not have the right to Transfer any of its oil and gas leasehold interests in any Joint Lease except (i) to the extent Total is exercising its rights under Section 6.2.1 as a Tag Offeree or (ii) for Transfers of oil and gas leasehold interests in the Joint Leases on which a well has been drilled. After the second anniversary of the Effective Date, Total shall have the right (subject to any transfer restrictions imposed by any applicable Operating Agreement) to freely Transfer any of its interests in the oil and gas leasehold interests in the Joint Leases.

6.2                                 Tag Along

6.2.1                        If a Party or any of its Affiliates (the “Transferor”) proposes to Transfer any of its oil and gas leasehold interests in any Joint Lease (other than with respect to the Sonangol Interest or the BHP Interest) to any Person (other than to an Affiliate) (the “Tag-Along Transferee”), then such Transferor shall send written notice of such proposed Transfer (which shall include a time and place designated for the closing of such purchase) of such third party offer (the “Tag-Along Notice”) to the other Party (the “Tag Offeree”) at least thirty (30) business days prior to effecting such Transfer. The Tag Offeree shall then have the irrevocable right (a “Tag-Along Right”), exercisable by delivery of an irrevocable notice to the Transferor at any time within twenty (20) business days after receipt of the Tag- Along Notice, to participate in such Transfer by selling the Tag Offeree’s Tag Along Share of the applicable oil and gas leasehold interests proposed to be Transferred, on substantially the same terms (including with respect to representations, warranties and indemnification) as the Transferor.

6.2.2                        If the Tag Offeree has exercised its Tag-Along Right and the Tag-Along Transferee is unwilling to purchase all of the oil and gas leasehold interests proposed to be Transferred by the Transferor and the exercising Tag Offeree, then the Transferor and the exercising Tag Offeree shall reduce, based on their respective Tag Along Share, the oil and gas leasehold interests that each otherwise would have sold so as to permit the Transferor and the exercising Tag Offeree to sell that portion of the oil and gas leasehold interests (determined in accordance with their Tag Along Share) that the proposed Tag-Along Transferee is willing to purchase.

6.2.3                        The Tag Offeree and the Transferor shall sell to the Tag-Along Transferee all of the oil and gas leasehold interests proposed to be Transferred by them, at not less than the price and upon terms and conditions, if any, not more favorable, individually and in the aggregate, to the Tag-Along Transferee than those in the Tag-Along Notice at the time and place provided for the closing in the Tag-Along

15

Notice, or at such other time and place as the Tag Offerees, the Transferor and the Tag-Along Transferee shall agree.

6.2.4                        If the Tag Offeree has exercised its Tag-Along Right, neither Party shall exercise its preferential right to purchase under the applicable Operating Agreement with respect to the oil and gas leasehold interests in the subject Joint Lease.

ARTICLE 7. TERM AND TERMINATION

7.1                                 Term.

The term of this Agreement (the “Agreement Term”) shall commence on the Effective Date and shall continue until the tenth anniversary of the Effective Date, and thereafter this Agreement shall continue for successive one-year periods unless either Party notifies the other Party at least thirty (30) days prior to the end of any such one-year period ending on an anniversary of the Effective Date that it elects for this Agreement not to continue; provided, that this Agreement shall terminate earlier upon an Event of Default or a Change of Control Election (defined below) under this Agreement.

7.2                                 Event of Default.

For the purposes of this Agreement, an “Event of Default” means:

(a)                                  a default by any Party in the observance or performance in any material respect of any of its material obligations hereunder with such default continuing for thirty (30) days after written notice is received from the other Party specifying the default and demanding that the same be remedied; or

(b)                                 an entry of a decree or order which remains in force, undischarged or unstayed for sixty (60) days relating to any Party by a court having jurisdiction (i) granting relief under Title 11 of the United States Code; (ii) approving as properly filed a petition seeking reorganization of such Party under Title 11 of the United States Code, or any other state or federal law; (iii) for the appointment of a receiver or liquidator or trustee in bankruptcy or insolvency of such Party or its property; (iv) appointing a custodian, trustee, receiver or agent with authorization to take charge of a material portion of such Party’s property for the purpose of enforcing a lien against such property; or (v) for the winding up or liquidation of the affairs of such Party; or

(c)                                  any Party having taken any of the following actions: (A) taking steps to institute proceedings or consenting to the institution of proceedings under any state or federal law relating to debtor rehabilitation, insolvency, bankruptcy, liquidation or reorganization, including specifically Title 11 of the United States Code; (B) consenting to the appointment of a receiver,

16

liquidator or trustee in bankruptcy or other insolvency proceedings of it or of its property or any substantial portion of its property; (C) procuring, permitting or suffering the appointment of a custodian, trustee, receiver or agent with authorization to take charge of a material portion of its property or for the purposes of enforcing a lien against such property; (D) making an assignment for the benefit of creditors, or admitting it is generally not able to pay its debts as they become due; or (E) failing to pay its material debts as they become due; or

(d)                                 with respect to Cobalt only, and at Total’s option, at least of two of Joseph H. Bryant, James W. Farnsworth and James H. Painter cease to be employed by Cobalt; or

(e)                                  with respect to Total only, and at Cobalt’s option, for any period of three (3) consecutive years after the Obligation Well Program Term:

(i) if Total has made different elections than Cobalt on more than fifty percent (50%) of all AFEs issued under any applicable Operating Agreement; or

(ii) if Total has elected not to participate in more than fifty percent (50%) of the activities that require a material expenditure of Non-OA/Administrative GoM Expenses on the Work Program and Budget, and Cobalt performed such activities and incurred all of the related Non-OA/Administrative GoM Expenses; or

(iii) if Total has failed to reasonably nominate experienced Secondees for at least the minimum number of Secondee positions offered by Cobalt in the Combined Operations Team pursuant to Section 4.1.2; or

(g)                                 if an event of default under and as defined in the Exchange Agreement has occurred and is continuing, and a Party is not in default thereunder, at the option of such non-defaulting Party.

7.3                                 Change of Control Election.

If any company whose primary business is exploration and production of oil and gas acquires (directly or indirectly through one or more Affiliates) more than 50% (whether in one or more transactions) of the voting interests (or similar rights granting the acquiring entity power to direct the management or policies of Cobalt) in Cobalt (a “Specified Change of Control”), then at Total’s option, Total shall have the right to elect to terminate this Agreement by notice to the acquiring company, such termination to be effective immediately upon receipt of such notice (a “Change of Control Election”).

17

7.4                                 Effect of Termination.

7.4.1                        Termination of the Agreement Term for any reason shall not relieve any Party of any obligation arising prior to such termination or as a result of any operation or activity conducted prior to such termination.

7.4.2                        Notwithstanding the preceding, the provisions of Section 6.1.5 and Article 8 (Miscellaneous) shall survive the termination of this Agreement until fully performed.

ARTICLE 8. MISCELLANEOUS

8.1                                 Conflict/Priority of Agreements. If there is a conflict between this Agreement and/or the Exchange Agreement and applicable Operating Agreement, the Exchange Agreement controls first. Then, this Agreement controls as between the Parties over the applicable Operating Agreement.

8.2                                 Confidentiality. Each Party agrees to maintain, and to cause its respective Affiliates to maintain, as strictly confidential and not to disclose to any third party the existence of this Agreement, the terms hereof and the Confidential Work Product, except as expressly provided hereunder but subject to any applicable Operating Agreement or applicable law, for a period commencing on the Effective Date and extending for an additional period of two (2) years after the termination of the Agreement unless disclosed by the mutual agreement of the Parties; provided, however, that (i) either Party may disclose Confidential Work Product to any potential bona fide purchaser that has agreed in writing to hold such information confidential, and (ii) Cobalt may disclose to any third party Confidential Work Product that is produced, acquired or developed as a result of the incurrence by Cobalt of Non-OA/Administrative GoM Expenses in which Total elected not to participate pursuant to Section 3.2 of this Agreement. Each Party agrees to treat the disclosure of the Confidential Work Product in the same manner as it treats its own confidential information. Cobalt shall obtain from its limited partners (other than members of Cobalt’s executive management team) properly executed confidentiality agreements in the form attached as Exhibit “F” hereto.

8.3                                 Severability. If any term or other provision of this Agreement is invalid, illegal or incapable of being enforced by any rule of applicable law or public policy, all other conditions and provisions of this Agreement shall nevertheless remain in full force and effect so long as the economic or legal substance of the transactions contemplated hereby is not affected in any manner materially adverse to any Party. Upon such determination that any term or other provision is invalid, illegal or incapable of being enforced, the Parties shall negotiate in good faith to modify this Agreement so as to effect the original intent of the Parties as closely as possible in an acceptable manner to the end that transactions contemplated hereby are fulfilled to the greatest extent possible.

8.4                                 Notices. All notices or other written communication required between the Parties and required by any of the provisions of this Agreement, unless otherwise specifically

18

provided, shall be given in writing by mail, postage or charges prepaid, and addressed to the Party to whom the notice is given as follows:

If to Cobalt:

Cobalt International Energy, L.P.

Two Post Oak Central

1980 Post Oak Blvd., Suite 1200

Houston, Texas 77056

Attention: Lynne L. Hackedorn, Land Manager

If to Total:

TOTAL E&P USA, INC.

1201 Louisiana, Suite 1800

Houston, Texas 77002

Attention: Eric Bonnin, Vice President Business Development & Strategy

or to such other address within the continental limits of the United States specified by a Party giving the other Party hereto written notice in accordance with this Section. Alternatively, notice may be given by personal delivery in writing to the Parties at their respective addresses as set forth above. Notice shall be deemed given on the date of service or transmission if personally served; provided, that if such service is not on a business day or is after normal business hours, then such notice shall be deemed given on the next business day. Notice otherwise sent as provided herein shall be deemed given on the next business day following timely delivery of such notice to a reputable air courier service with an order for next day delivery.

8.5                                 Further Assurances. Each Party hereto shall, from time to time, do and perform such further acts and execute and deliver such further instruments, assignments and documents as may be required or reasonably requested by the other Party to establish, maintain or protect the respective rights and remedies of the Parties hereto and to carry out and effect the intentions and purposes of this Agreement.

8.6                                 No Waiver. The failure of any Party hereto to insist upon strict performance of any provision hereof shall not constitute a waiver of, or estoppel against asserting, the right to require such performance in the future, nor shall a waiver or estoppel in any one instance constitute a waiver or estoppel with respect to a later breach of a similar nature or otherwise.

8.7                                 Waiver of Certain Damages. Each Party irrevocably waives and agrees not to seek indirect, consequential, punitive or exemplary damages of any kind in connection with any dispute arising out of or related to this Agreement or the breach hereof.

19

8.8                                 Construction. The headings in this Agreement are inserted for convenience and identification only and are not intended to describe, interpret, define or limit the scope, extent or intent of this Agreement or any provision hereof. Whenever the context requires, the gender of all words used in this Agreement shall include the masculine, feminine, and neuter, and the number of all words shall include the singular and the plural. In the event of a conflict between this Agreement and the exhibits, this Agreement shall control.

8.9                                 Entire Agreement. This Agreement (including the exhibits to this Agreement), the Exchange Agreement and any applicable Operating Agreement, which incorporates all prior understandings relating to the subject matter hereof, set forth the entire agreement of the Parties with respect to the matters set forth herein and shall not be modified except by written instrument executed by all Parties.

8.10                           Binding Effect. Subject to the other provisions of this Agreement, all of the terms and provisions hereof shall be binding upon and inure to the use and benefit of the Parties and their respective heirs, successors, legal representatives and assigns.

8.11                           GOVERNING LAW. THE PROVISIONS OF THIS AGREEMENT AND THE RELATIONSHIP OF THE PARTIES SHALL BE GOVERNED AND INTERPRETED ACCORDING TO FEDERAL LAWS AND LAWS OF THE STATE OF TEXAS WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS THAT WOULD REFER THE MATTER TO THE LAWS OF ANOTHER JURISDICTION.

8.12                           Dispute Resolution. Any dispute, controversy or claim between the Parties arising out of or in connection with this Agreement, including any question as to its existence, enforceability, validity, interpretation or termination, shall be resolved pursuant to the dispute resolution procedures set forth in Exhibit E.

8.13                           Drafting of Agreement. Each Party acknowledges that it and its attorneys have contributed to the drafting of this Agreement. It is expressly agreed that this Agreement shall not be construed against any Party on the basis of who drafted this Agreement or who supplied the form of Agreement. Each Party agrees that this Agreement has been purposefully drawn and correctly reflects its understanding of the transactions contemplated hereby. Each Party further acknowledges that it has been advised and represented by its own counsel in negotiating and entering into this Agreement.

8.14                           Multiple Originals. This Agreement may be executed in multiple originals, each of which shall be deemed an original but all of which shall constitute but one Agreement.

[Remainder of Page Left Blank]

20

COBALT INTERNATIONAL ENERGY, L.P.

Signature Page to

Gulf of Mexico Program Management and AMI Agreement