Exhibit 5.1

Texas New York Washington, DC Connecticut Dubai Kazakhstan London Bracewell & Giuliani LLP 711 Louisiana Street Suite 2300 Houston, Texas 77002-2770   713.223.2300 Office 713.221.1212 Fax   bgllp.com

February 22, 2012

ConocoPhillips

600 North Dairy Ashford

Houston, Texas 77079

Ladies and Gentlemen:

We have acted as counsel to ConocoPhillips, a Delaware corporation (“ConocoPhillips”), in connection with the preparation of a Registration Statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by ConocoPhillips, ConocoPhillips Company, a Delaware corporation (“CPCo”), and ConocoPhillips Trust I and ConocoPhillips Trust II, each a statutory Delaware trust (the “Trusts”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the offering of securities that may be issued and sold by ConocoPhillips, CPCo and the Trusts from time to time pursuant to Rule 415 under the Act, certain legal matters in connection with such securities are being passed upon for you by us. Such securities include (a) ConocoPhillips’ unsecured senior debt securities (the “Senior Debt Securities”) guaranteed by CPCo (the “Senior Debt Guarantees”); (b) ConocoPhillips’ unsecured subordinated debt securities (the “Subordinated Debt Securities” and, together with the Senior Debt Securities, the “Debt Securities”); (c) shares of common stock, par value $.01 per share, of ConocoPhillips (“Common Stock”) and the related preferred share purchase rights (the “Rights”) to be issued pursuant to the Rights Agreement, dated as of June 30, 2002 (the “Rights Agreement”), between ConocoPhillips and Mellon Investor Services LLC, as rights agent (the “Rights Agent”); (d) shares of preferred stock, par value $.01 per share, of ConocoPhillips (“Preferred Stock”); (e) warrants to purchase other securities (“Warrants”); (f) depositary shares representing Preferred Stock (“Depositary Shares”); (g) stock purchase contracts of ConocoPhillips (“Stock Purchase Contracts”); (h) stock purchase units of ConocoPhillips, consisting of (1) a Stock Purchase Contract and (2) a beneficial interest in Senior Debt Securities, Subordinated Debt Securities, Trust Securities (as defined below) or debt obligations of third parties securing the holder’s obligation to purchase Common Stock or Preferred Stock under the Stock Purchase Contracts (“Stock Purchase Units”); (i) preferred securities of the Trusts (the “Trust Securities”); and (j) ConocoPhillips’ guarantees with respect to the Trust Securities (the “Trust Guarantees”). The Debt Securities, Senior Debt Guarantees, Common Stock, Rights, Preferred Stock, Warrants, Depositary Shares, Stock Purchase Contracts, Stock Purchase Units and Trust Guarantees are collectively referred to herein as the “Securities.” At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

ConocoPhillips

February 22, 2012

Page 2

Each series of Senior Debt Securities and the related Senior Debt Guarantees are to be issued pursuant to the Indenture, dated as of October 9, 2002, among ConocoPhillips, as issuer, CPCo, as guarantor, and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Senior Indenture”); and each series of Subordinated Debt Securities are to be issued pursuant to an indenture to be entered into between ConocoPhillips, as issuer, and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Subordinated Indenture” and, together with the Senior Indenture, the “Indentures”). Each Indenture is to be supplemented, in connection with the issuance of each such series, by a supplemental indenture, officers’ certificate or other writing thereunder establishing the form and terms of such series. Each Trust Guarantee is to be issued pursuant to a guarantee agreement to be entered into between ConocoPhillips and The Bank of New York Mellon Trust Company, N.A., as guarantee trustee thereunder (each, a “Guarantee Agreement”).

We have examined originals, or copies certified or otherwise identified, of (i) the Registration Statement, (ii) ConocoPhillips’ Amended and Restated Certificate of Incorporation and By-laws and CPCo’s Restated Certificate of Incorporation and By-laws, in each case as amended to date (the “Charter Documents” of such entity), (iii) the Senior Indenture, (iv) the form of Subordinated Indenture (in the form to be filed as an exhibit to the Registration Statement), (v) corporate records of ConocoPhillips and CPCo, including minute books of ConocoPhillips and CPCo, as furnished to us by them and (vi) such other instruments, documents and records as we have deemed necessary and relevant for the purposes hereof. We have relied upon certificates of officers of ConocoPhillips and CPCo and of public officials as to certain matters of fact relating to this opinion and have made such investigations of law as we have deemed necessary and relevant as a basis hereof. In such examinations, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents, certificates and records submitted to us as originals, the conformity to authentic original documents, certificates and records of all documents, certificates and records submitted to us as copies, and the truthfulness of all statements of fact contained therein. In making our examination of executed documents or documents to be executed, we have assumed that they constitute or will constitute valid, binding and enforceable obligations of all parties thereto other than the Company and CPCo.

In connection with this opinion, we have assumed that:

(a) the Registration Statement and any amendments thereto (including post-effective amendments) will have become effective under the Act;

(b) a prospectus supplement will have been prepared and filed with the Commission describing the Securities offered thereby;

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ConocoPhillips

February 22, 2012

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(c) all Securities will be offered, issued and sold in compliance with applicable securities laws and in the manner stated in the Registration Statement and the applicable prospectus supplement;

(d) the Board of Directors of ConocoPhillips and, if applicable, CPCo or, to the extent permitted by the General Corporation Law of the State of Delaware and the Charter Documents of ConocoPhillips and, if applicable, CPCo, a duly constituted and acting committee thereof (such Board of Directors of ConocoPhillips or committee thereof being hereinafter referred to as the “Board”) will have taken all necessary corporate action to authorize the issuance of the Securities and any other Securities issuable on the conversion, exchange, redemption or exercise thereof, and to authorize the terms of the offering and sale of such Securities and related matters;

(e) a definitive purchase, underwriting or similar agreement with respect to any Securities offered will have been duly authorized and validly executed and delivered by ConocoPhillips and the other parties thereto (the “Purchase Agreement”);

(f) any securities issuable upon conversion, exchange, redemption or exercise of any Securities being offered will have been duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange, redemption or exercise;

(g) all Securities, and any certificates or Receipts (as defined below) in respect thereof, will be delivered either (i) in accordance with the provisions of the applicable Purchase Agreement approved by the Board upon payment of the consideration therefor provided for therein or (ii) upon conversion, exchange, redemption or exercise of any other Security, in accordance with the terms of such Security or the instrument governing such Security providing for such conversion, exchange, redemption or exercise as approved by the Board, for the consideration approved by the Board;

(h) in the case of shares of Common Stock or Preferred Stock, certificates representing such shares will have been duly executed, countersigned, registered and delivered, or if uncertificated, valid book-entry notations will have been made in the share register of ConocoPhillips, in each case in accordance with the provisions of the Charter Documents of ConocoPhillips; there will be sufficient shares of Common Stock or Preferred Stock authorized under such Charter Documents and not otherwise issued or reserved for issuance; and the purchase price therefor payable to ConocoPhillips or, if such shares are issuable on the conversion, exchange, redemption or exercise of another Security, the consideration payable to ConocoPhillips for such conversion, exchange, redemption or exercise will not be less than the par value of such shares, in the case of shares of Common Stock, or the lesser of such purchase price or such consideration, as the case may be, or the amount of such purchase price or such consideration, as the case may be, timely determined by the Board to constitute the stated capital applicable to such shares, in the case of shares of Preferred Stock;

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ConocoPhillips

February 22, 2012

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(i) in the case of Rights, the Board, after fully informing itself with respect to the Rights Agreement and the Rights and after giving due consideration to all relevant matters, will have determined that the issuance of the Rights under the Rights Agreement would be in the best interests of ConocoPhillips and its stockholders; and the Rights Agreement has been duly authorized, executed and delivered by the Rights Agent;

(j) in the case of shares of Preferred Stock of any series, the Board will have taken all necessary corporate action to designate and establish the terms of such series and will have caused a certificate of designations respecting such series and conforming to ConocoPhillips’s Amended and Restated Certificate of Incorporation and By-laws and the Delaware General Corporation Law to be prepared and filed with the Secretary of State of the State of Delaware;

(k) in the case of Warrants, the Board will have taken all necessary corporate action to authorize the creation of and the terms of such Warrants and the issuance of the Securities to be issued pursuant thereto and to approve the warrant agreement relating thereto; such warrant agreement will have been duly executed and delivered by ConocoPhillips and the warrant agent thereunder appointed by ConocoPhillips; neither such Warrants nor such warrant agreement will include any provision that is unenforceable; and such Warrants or certificates representing such Warrants will have been duly executed, countersigned, registered and delivered in accordance with the provisions of such warrant agreement and the applicable definitive purchase, underwriting or similar agreement approved by the Board upon payment of the consideration therefor provided for therein;

(l) in the case of Depositary Shares, the Board will have taken all necessary corporate action to establish the terms of the Depositary Shares; the action with respect to the Preferred Stock underlying such Depositary Shares referred to in paragraph (i) above will have been taken; a depositary agreement (the “Depositary Agreement”) relating to the Depositary Shares and the related depositary receipts evidencing such Depositary Shares (“Receipts”) will have been duly authorized and validly executed and delivered by ConocoPhillips and a bank or trust company to be selected by ConocoPhillips, as depositary (the “Depositary”), and such Depositary Agreement and such Receipts will not include any provision that is unenforceable; the shares of Preferred Stock underlying such Depositary Shares will have been deposited with the Depositary under the applicable Depositary Agreement; and the Depositary Receipts will have been duly executed, countersigned, registered and delivered in accordance with the applicable Depositary Agreement and the applicable definitive purchase, underwriting or similar agreement approved by the Board upon payment of the consideration therefor provided for therein;

(m) in the case of a series of Subordinated Debt Securities, the trustee is qualified to act as trustee under the Subordinated Indenture and an indenture substantially in the form of the Subordinated Indenture will have been duly executed and delivered by ConocoPhillips and the trustee thereunder;

(n) in the case of a series of Debt Securities issuable under an Indenture:

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ConocoPhillips

February 22, 2012

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• the Board will have taken all necessary corporate action to designate and establish the terms of such Debt Securities in accordance with the terms of the Indenture under which such Debt Securities will be issued, and such Debt Securities will not include any provision that is unenforceable;

• the Indenture under which such Debt Securities will be issued will have become qualified under the Trust Indenture Act of 1939, as amended; and

• forms of Debt Securities, including, if applicable, the related Senior Debt Guarantees, complying with the terms of the Indenture under which such Debt Securities will be issued and evidencing such Debt Securities and, if applicable, the related Senior Debt Guarantees will have been duly executed, authenticated, issued and delivered in accordance with the provisions of such Indenture and the applicable definitive purchase, underwriting or similar agreement approved by the Board upon payment of the consideration therefor provided for therein;

(o) in the case of each Trust Guarantee, the Board will have taken all necessary corporate action to establish the terms thereof; a guarantee agreement substantially in the form of the Guarantee Agreement will have been duly executed and delivered by ConocoPhillips and the trustee thereunder; such guarantee agreement will have become qualified under the Trust Indenture Act of 1939, as amended, and will not contain any provision that is unenforceable; and such Trust Guarantee will have been duly issued and delivered in accordance with the provisions of such guarantee agreement;

(p) in the case of Stock Purchase Contracts, the Board will have taken all necessary corporate action to establish the terms thereof and to approve the purchase contract agreement relating thereto; such Stock Purchase Contracts and purchase contract agreement will have been duly executed and delivered by the parties thereto; and neither such Stock Purchase Contracts nor such purchase contract agreement will include any provision that is unenforceable;

(q) in the case of Stock Purchase Units, the Board will have taken all necessary corporate action to establish the terms of such Stock Purchase Units and the terms of the Securities, if any, such Stock Purchase Units include; the action with respect to the Stock Purchase Contracts included in such Stock Purchase Units referred to in paragraph (o) above will have been taken; if such Stock Purchase Units include Trust Securities, such Trust Securities will be legal, valid and binding obligations of the applicable Trust, enforceable against the applicable Trust in accordance with their terms; if such Stock Purchase Units include securities other than Securities or Trust Securities, such other securities will have been duly and validly executed, issued and delivered by the issuer thereof and will be legal, valid and binding obligations of such issuer, enforceable against such issuer in accordance with their respective terms; and no agreement or other instrument establishing such Stock Purchase Units or defining the rights of the holders of such Stock Purchase Units will contain any provision that is unenforceable; and

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ConocoPhillips

February 22, 2012

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(r) all necessary actions shall be taken by ConocoPhillips and CPCo so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon ConocoPhillips and CPCo and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over ConocoPhillips and CPCo.

On the basis of the foregoing, and subject to the assumptions, limitations and qualifications hereinafter set forth, we are of the opinion that:

1. The shares of Common Stock and Preferred Stock included in the Securities will, when issued, have been duly authorized by all necessary corporate action on the part of ConocoPhillips and validly issued and will be fully paid and nonassessable; and upon such issuance of Common Stock, the Rights will have been validly issued.

2. The Warrants and the Depositary Shares included in the Securities will, when issued, have been duly authorized by all necessary corporate action on the part of ConocoPhillips and validly issued.

3. The Debt Securities, Trust Guarantees, Stock Purchase Contracts and Stock Purchase Units included in the Securities will, when issued, constitute legal, valid and binding obligations of ConocoPhillips, enforceable against ConocoPhillips in accordance with their respective terms.

4. Each Senior Debt Guarantee of CPCo relating to any Senior Debt Securities included in the Securities will, when issued, constitute a legal, valid and binding obligation of CPCo, enforceable against CPCo in accordance with its terms.

The foregoing opinion is based on and is limited to the General Corporation Law of the State of Delaware and the relevant contract law of the State of New York. We express no opinion as to any other laws, statutes, regulations or ordinances, including federal and state securities (or “blue sky”) laws. We are not admitted to practice law in the State of Delaware.

Our opinion that any document or Security is a legal, valid and binding obligation of ConocoPhillips or CPCo is subject to (i) applicable bankruptcy, insolvency, reorganization, arrangement, fraudulent conveyance, moratorium or other similar laws relating to or affecting the rights of creditors generally, (ii) general principles of equity, including without limitation concepts of materiality, reasonableness, good faith and fair dealing, and the possible unavailability of specific performance or injunctive relief and limitation of rights of acceleration, regardless of whether such enforceability is considered in a proceeding in equity or at law and (iii) limitations of rights to indemnification, exculpation and contribution which may be limited by applicable law or equitable principles. We also express no opinion regarding the effectiveness of any waiver of stay, extension or usury laws or of unknown future rights, and we express no opinion regarding severability provisions.

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ConocoPhillips

February 22, 2012

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In connection with our opinion set forth in paragraph (1) above with respect to the Rights, we note that the question whether the Board might be required to redeem the Rights at some future time will depend upon the facts and circumstances existing at that time and, accordingly, is beyond the scope of such opinion.

You have informed us that you intend to issue Securities from time to time on a delayed or continuous basis. This opinion is limited to the laws referred to above as in effect on the date hereof. We understand that prior to issuing any Securities pursuant to the Registration Statement (i) you will advise us in writing of the terms thereof and (ii) you will afford us an opportunity to review the documents pursuant to which such Securities are to be issued or sold (including the applicable offering documents) and you will file such supplement or amendment to this opinion (if any) as we may advise you may be necessary or appropriate.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our Firm under the heading “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving such consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission.

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein.

Very truly yours,

/s/ Bracewell & Giuliani LLP

Bracewell & Giuliani LLP

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