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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FOR IMMEDIATE RELEASE          Contact - Guy T. Marcus
September 24, 1996                       Vice President-Inv. Rel.
                                         (214) 978-2691

          HALLIBURTON TO REALIGN BUSINESS SEGMENTS

     DALLAS,  Texas -- Halliburton  Company  (NYSE-HAL)  today announced that it
will realign  business  units within its two business  segments  during the 1996
fourth  quarter in order to better meet the growing  customer needs for complete
arrays of integrated energy services.

     The Energy Services business segment will be restructured to consist of its
traditional   Halliburton   Energy  Services  lines  of  business  and  add  the
capabilities  of  Brown & Root  Energy  Services,  Landmark  Graphics  and a new
company to be formed and be responsible for  Halliburton's  recently  introduced
contract-to-produce  business.  Brown & Root Energy  Services,  with revenues of
about  $540  million  during  the first six  months of 1996,  is  currently  the
upstream  oil and gas  services  business  unit  associated  with the  company's
engineering and construction business segment. Halliburton plans to complete the
acquisition of Landmark Graphics,  a leading supplier of integrated  exploration
and production  information  systems and professional  services to the petroleum
industry,  in October 1996. The new  contract-to-produce  organization  is being
formed to create new business  opportunities  for  development,  production  and
operations of oil and gas fields by  integrating  Brown & Root Energy  Services'

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engineering,  construction and project management  capabilities with Halliburton
Energy Services' subsurface expertise.

     Ken  LeSuer,  60,  has been  named  chief  executive  officer of the Energy
Services  business  segment.  LeSuer has 36 years of experience with Halliburton
and was  previously  the president and chief  executive  officer of  Halliburton
Energy  Services.  W.J. (Zeke)  Zeringue,  Jr., 47, has been promoted from chief
operating officer to president of the Halliburton Energy Services business unit.
Larry Farmer, 56, will continue as president of Brown & Root Energy Services. He
joined the company 20 years ago and has experience in the worldwide  business of
engineering and construction of oil and gas production facilities and pipelines.
Bob Peebler,  49, will  continue as  president  and chief  executive  officer of
Landmark  following the acquisition of Landmark.  Peebler has been the company's
president and chief executive officer since 1992. Norman Chambers,  47, has been
named to the  position of  president  of the new  contract-to-produce  business.
Chambers has eleven years of service with the company, most recently as managing
director of Brown & Root Energy Services.

     Dave Lesar, 43, will become president and chief executive  officer of Brown
& Root in  addition  to his  duties  as  Halliburton  Company's  executive  vice
president  and chief  financial  officer.  Tommy  Knight  will be  taking  early
retirement from Brown & Root. Lesar will be forming a team of experienced  Brown

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& Root  management  to  establish  a new  organizational  structure  capable  of
positioning  Brown & Root for future  growth and  success.  Lesar will remain in
this role through the reorganization and until a successor is named.

     The engineering and construction  business segment will continue to consist
of the business  operations  of Brown & Root,  Inc.,  with the  exception of the
Brown  &  Root  Energy  Services  business.  These  include  the  petroleum  and
chemicals, pulp and paper, manufacturing, civil, environmental,  maintenance and
government businesses.

     Dick  Cheney,  Halliburton  Company's  chairman  of  the  Board  and  chief
executive officer,  said, "I believe that combining all of Halliburton's  energy
services  businesses  under a common  management  and operating  structure  will
enable the company to maximize  utilization of its full complement of skills and
expertise.  The company's core  competencies  and ability to integrate and align
with customers is not matched by any competitor."

     Halliburton  Company  is one  of the  world's  largest  diversified  energy
services, engineering, maintenance, and construction companies. Founded in 1919,
Halliburton  provides a broad range of energy services and products,  industrial
and marine engineering and construction services.

                                      # # #

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