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)

                               SEPTEMBER 24, 1996

                               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. 73-0271280

                               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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         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  September  24, 1996,  registrant  issued a press  release  entitled
Halliburton to Realign Business Segments  pertaining,  among other things, to an
announcement that registrant will realign business units within its two business
segments during the 1996 fourth quarter.  Registrant's  Energy Services  segment
will be restructured to consist of its traditional  Halliburton  Energy Services
lines of business and add Brown & Root Energy Services,  Landmark Graphics and a
new company to be formed to be responsible for registrant's  contract-to-produce
business.  Registrant plans to complete the acquisition of Landmark  Graphics in
October 1996.  Ken LeSuer has been named chief  executive  officer of the Energy
Services  business  segment.  W. J. (Zeke)  Zeringue,  Jr. has been  promoted to
president  of  Halliburton  Energy  Services.  Larry  Farmer  will  continue  as
president  of  Brown & Root  Energy  Services.  Bob  Peebler  will  continue  as
president and chief executive  officer of Landmark  following the acquisition of
Landmark.   Norman   Chambers   has  been   named  as   president   of  the  new
contract-to-produce  business.  Dave  Lesar  will  become  president  and  chief
executive  officer of Brown & Root in  addition  to his  duties as  registrant's
executive vice  president and chief  financial  officer.  Tommy Knight will take
early retirement from Brown & Root.

         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 September 24, 1996.




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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: September 25, 1996                      By: _______________________
                                                     Robert M. Kennedy
                                                     Vice President-Legal

























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                                EXHIBIT INDEX



Exhibit                                                         Sequentially
Number                      Description                         Numbered Page

    20                      Press Release of
                            September 24, 1996                      5 of 7
                            Incorporated by Reference





























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