Exhibit 5.1

March 8, 2016

ConocoPhillips

ConocoPhillips Company

c/o ConocoPhillips

600 North Dairy Ashford

Houston, Texas 77079

Re:                 ConocoPhillips Company—Offering of Debt Securities

Ladies and Gentlemen:

We have acted as counsel for ConocoPhillips, a Delaware corporation (the “Company”), and ConocoPhillips Company, a Delaware corporation (“CPCo”), in connection with the registration under the Securities Act of 1933, as amended, of $1,250,000,000 aggregate principal amount of CPCo’s 4.200% Notes due 2021 (the “2021 Notes”), $1,250,000,000 aggregate principal amount of CPCo’s 4.950% Notes due 2026 (the “2026 Notes”) and $500,000,000 aggregate principal amount of CPCo’s 5.950% Notes due 2046 (the “2046 Notes” and, together with 2021 Notes and the 2026 Notes, the “Notes”), in each case including the related guarantees by the Company (the “Guarantees”), pursuant to a Prospectus Supplement dated March 3, 2016 (the “Prospectus Supplement”).

In connection with this opinion, we have reviewed such matters of law and examined original, certified, conformed or photographic copies of such other documents, records, agreements and certificates as we have deemed necessary as a basis for the opinions hereinafter expressed.  In such review we have assumed the genuineness of signatures on all documents submitted to us as originals and the conformity to original documents of all copies submitted to us as certified, conformed or photographic copies.  We have relied, as to the matters set forth therein, on certificates of public officials.  As to certain matters of fact material to this opinion, we have relied, without independent verification, upon certificates of the Company and CPCo, and of certain officers of the Company and CPCo.

We have assumed that the execution and delivery of, and the performance of all obligations under, the Indenture dated as of May 18, 2015 (the “Indenture”), between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), has been duly authorized by all requisite action by the Trustee, and that the Indenture was duly executed and

delivered by, and is a valid and binding agreement of, the Trustee, enforceable against the Trustee in accordance with its terms.

This opinion is limited in all respects to the laws of the State of New York and the corporate law of the State of Delaware (which includes the Delaware General Corporation Law, applicable provisions of the Delaware Constitution and reported judicial interpretations concerning those laws), and no opinion is expressed with respect to the laws of any other jurisdiction or any effect which such laws may have on the opinions expressed herein.  This opinion is limited to the matters stated herein, and no opinion is implied or may be inferred beyond the matters expressly stated herein.

Based upon the foregoing, and subject to the assumptions, qualifications and limitations set forth herein, we are of the opinion that, upon the issuance and sale thereof as described in the Prospectus Supplement and, when executed by CPCo and the Company, as applicable, and duly authenticated by the Trustee in accordance with the terms of the Indenture, the Notes and the Guarantees, respectively, will be valid and binding obligations of CPCo and the Company, as applicable, enforceable against CPCo and the Company, as applicable, in accordance with their terms, subject, as to the enforcement of remedies, to bankruptcy, insolvency, reorganization, moratorium and similar laws affecting the rights and remedies of creditors generally, and the effects of general principles of equity.

This opinion is given as of the date hereof, and we assume no obligation to advise you after the date hereof of facts or circumstances that come to our attention or changes in law that occur which could affect the opinions contained herein.  This letter is being rendered solely for the benefit of the Company in connection with the matters addressed herein.  This opinion may not be furnished to or relied upon by any person or entity for any purpose without our prior written consent.

We hereby consent to the filing of this opinion as an exhibit to the current report on Form 8-K filed on March 8, 2016 and to the reference to us under the caption “Legal Matters” in the Prospectus Supplement.

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