SECURITIES AND EXCHANGE COMMISSION

                     Washington, D.C. 20549



                            FORM 8-K

                         CURRENT REPORT

             PURSUANT TO SECTION 13 OR 15(d) OF THE
                 SECURITIES EXCHANGE ACT OF 1934

        DATE OF REPORT (date of earliest event reported)

                          MAY 28, 1997

                       Halliburton Company
     (Exact name of registrant as specified in its charter)

State or other             Commission          IRS Employer
jurisdiction               File Number         Identification
of incorporation                               Number

Delaware                     1-3492            No. 75-2677995

                       3600 Lincoln Plaza
                     500 North Akard Street
                    Dallas, Texas 75201-3391
            (Address of principal executive offices)

                 Registrant's telephone  number,
               including area code - 214/978-2600




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               The Exhibit Index Appears on Page 4


     INFORMATION TO BE INCLUDED IN REPORT

Item 5.   Other Events

      The  registrant may, at its option, report under this  item
any  events,  with respect to which information is not  otherwise
called  for by this form, that the registrant deems of importance
to security holders.

      On May 28, 1997, registrant issued a press release entitled
Halliburton  to Acquire Kinhill Holdings pertaining, among  other
things,  to an announcement  that registrant's Brown &  Root  Pty
Ltd  business unit has offered to purchase for cash  all  of  the
outstanding  shares  of Kinhill Holdings Limited,  an  Australian
public company.  The offered cash purchase price is AUD 1.64  per
share  (about  $1.25  U.S.).   The consideration,  including  the
purchase of outstanding options and convertible notes, will total
about $34 million U.S.  The offer will be made by Brown & Root to
Kinhill   shareholders  within  the  next  few   days   and   the
shareholders  will  have 30 days to accept.   Brown  &  Root  has
already acquired control of 19.99 percent of the issued shares of
Kinhill as well as some convertible notes and an existing  option
to subscribe to 1,375,000 shares.

      The  foregoing summary is subject to the full text  of  the
press  release with respect thereto, a copy of which is  attached
hereto  as  Exhibit 20, which exhibit is incorporated  herein  by
reference.

Item 7.   Financial Statements and Exhibits

      List  below  the financial statements, pro forma  financial
information and exhibits, if any, filed as part of this report.

     (c)  Exhibits.

          Exhibit 20 - Press release dated May 28, 1997.












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                           SIGNATURES

      Pursuant to the requirements of the Securities Exchange Act
of  1934, the registrant has duly caused this report to be signed
on its behalf by the undersigned hereunto duly authorized.


                                   HALLIBURTON COMPANY




Date:  May 28, 1997                By: /s/ Susan S. Keith
                                   -----------------------------
                                     Susan S. Keith
                                     Vice President, Secretary and
                                     Corporate Counsel

























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                          EXHIBIT INDEX



Exhibit                                              Sequentially
Number                 Description                   Numbered Page

    20                 Press Release of
                       May 28, 1997                     5 of 6
                       Incorporated by Reference































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