EXHIBIT 5.1


                   [VINSON & ELKINS LETTERHEAD APPEARS HERE]


                                  June 3, 1999


Halliburton Company
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas  75201-3391

Ladies and Gentlemen:

     We acted as counsel for Halliburton Company, a Delaware corporation
("Halliburton"), in connection with Halliburton's registration statement on Form
S-4 (the "Registration Statement") relating to the offering, sale and delivery
of shares (the "Shares") of Halliburton's common stock, par value $2.50 per
share, pursuant to the proposed offer of Halliburton to acquire all the issued
ordinary share capital of PES (International) Limited, a corporation organized
under the laws of Scotland ("PES"), other than those shares now owned indirectly
by Halliburton.  Capitalized terms used but not defined in this opinion are
defined in the Registration Statement and are use herein with the same meanings
as ascribed to them therein.

     Before rendering our opinion, we examined certain of the corporate records
of Halliburton, including its Restated Certificate of Incorporation, certain
resolutions of the Board of Directors of Halliburton, the Registration Statement
and the exhibits thereto and such certificates of corporate officers of
Halliburton and governmental officials as we deemed necessary for the purposes
of this opinion.  As to matters of fact relevant to the opinions expressed
herein, and as to factual matters arising in connection with our examination of
the above described documents, we relied upon certificates and other
communications of corporate officers of Halliburton and governmental officials
without further investigation as to the facts set forth therein.

     Based upon the foregoing, we are of the opinion that the Shares have been
validly authorized for issuance and, upon issuance as described in the
Registration Statement, will be validly issued, fully paid and nonassessable.

     We hereby consent to the filing of this letter as an exhibit to the
Registration Statement.  By giving such consent, we do not admit that we are
within the category of persons whose consent is required under Section 7 of the
Securities Act of 1933, as amended, or the rules and regulations of the
Securities and Exchange Commission issued thereunder.  For purposes of the
foregoing opinions,


Halliburton Company
Page 2
_______, 1997

we assumed that the Shares will be offered, issued and sold in compliance with
all applicable state securities or Blue Sky laws.


                                    Very truly yours,

                                    /s/ VINSON & ELKINS L.L.P.

                                    VINSON & ELKINS L.L.P.