[Letterhead of Vinson & Elkins L.L.P.]
                                                                     Exhibit 8.2

                               November 12, 1999


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

            Subject: PES (International) Limited
            ------------------------------------

Gentlemen:

        We participated in the preparation of the registration statement on Form
S-4 with respect to the Recommended Offer by Halliburton Company for the
Ordinary Share Capital of PES (International) Limited, including the discussion
set forth in the Registration Statement under the heading "United States Federal
Tax Consequences."/1/

        We hereby affirm that the discussion and the legal conclusions with
respect to the United States federal tax matters set forth therein constitute
our opinion as to the material United States federal tax consequences of the
Offer and the Compulsory Acquisition to holders of PES Shares.

        We hereby consent to the use of our name in the Registration Statement
and to the filing of this opinion as part of the Registration Statement.


                                Very truly yours,


                                VINSON & ELKINS L.L.P.

________________________

     /1/Capitalized terms used but not defined herein have the meanings
ascribed to them in the Registration Statement.