[LETTERHEAD OF VINSON & ELKINS APPEARS HERE] August 1, 1997 EXHIBIT 5.1 Halliburton Company 3600 Lincoln Plaza 500 North Akard Street Dallas, Texas 75201-3391 Re: Halliburton Company; Debt Securities Ladies and Gentlemen: We are acting as counsel to Halliburton Company, a Delaware corporation (the "Company"), in connection with the offering, sale and delivery by it from time to time, in one or more series, of its debt securities (the "Debt Securities") with an aggregate initial offering price not to exceed $600,000,000 on terms to be determined at the time of offering. The offering, sale and delivery of the Debt Securities are being registered pursuant to the registration provisions of the Securities Act of 1933, as amended, by virtue of the Company's Registration Statement on Form S-3 to which this opinion is an exhibit. The Debt Securities are to be issued pursuant to the Second Senior Indenture dated as of December 1, 1996 between the Company and Texas Commerce Bank National Association, as trustee, as amended, supplemented and modified by the First and Second Supplemental Indentures dated as of December 5, 1996 and December 12, 1996, respectively (the "Second Senior Indenture"), or the Subordinated Indenture dated as of January 2, 1991 between the predecessor of the Company and Texas Commerce Bank National Association, as trustee, as amended, supplemented and modified by the First Supplemental Indenture dated as of December 12, 1996 among the Company, the Company's predecessor and the trustee (the "Subordinated Indenture"). The Second Senior Indenture and the Subordinated Indenture are herein referred to as the "Indentures". Capitalized terms used but not defined herein are defined in the Indentures and are used herein with the same meanings as ascribed to them therein. In our capacity as counsel to the Company, we examined the Registration Statement, the Prospectus and the Indentures. We also examined the certificate of incorporation and by-laws of the Company and the minutes of all meetings and all unanimous consents of the board of directors of the Company and any committees thereof relating to the authorization, issuance and sale of the Debt Securities. In addition, we examined and relied upon certificates and telegrams of public officials and certificates of officers of the Company and we made such other investigations and examined such other documents as we deemed necessary as a basis for the opinions hereinafter expressed. In the course of the foregoing investigations and examinations, we assumed the genuineness of all signatures on, and the authenticity of, all documents and instruments submitted to us as originals, the conformity to original documents of all documents submitted to us as copies and the due authorization, execution and delivery by the parties thereto of all documents and instruments examined by us. Based on the foregoing and subject to the qualifications set forth below, we are of the opinion that: (i) The Company has been duly incorporated and is validly existing as a corporation in good standing under the laws of the State of Delaware. (ii) The Indentures have been duly authorized, executed and delivered by the Company and (assuming each Indenture has been duly authorized, executed and delivered by the Trustee) constitute legal, valid and binding agreements of the Company, enforceable in accordance with their terms, except as enforcement thereof may limited by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting enforcement of creditors' rights generally, general equitable principles (whether considered in a proceeding in equity or at law) and an implied covenant of good faith and fair dealing. (iii) The Debt Securities, upon determination of the terms and provisions thereof pursuant to a Terms Certificate issued by the Company to the Trustee, will be duly authorized for issuance, and, when issued, authenticated and delivered pursuant to the provisions of the Indentures against payment of the consideration therefor, will constitute valid and legally binding obligations of the Company, enforceable in accordance with their terms, except as enforcement thereof may limited by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting enforcement of creditors' rights generally, general equitable principles (whether considered in a proceeding in equity or at law) and an implied covenant of good faith and fair dealing. The opinions herein expressed are limited to the federal laws of the United States, the laws of the States of Texas and New York and the General Corporation Law of the State of Delaware, all as in effect on the date hereof. We hereby consent to the reference to our Firm under the caption "Legal Opinions" in the Prospectus constituting a part of the Registration Statement. Very truly yours, Vinson & Elkins L.L.P.