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)

                                  APRIL 8, 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 April 8, 1996,  registrant  issued a press release entitled Alliance
Starts on  BP's 400 Million (pounds sterling) Schiehallion Project pertaining,  
among  other  things,  to  an  announcement  that  an  alliance  involving  BP, 
registrant's Brown & Root subsidiary,  Harland and Wolff,  Single Buoy  Moorings
and  Coflexip Stena Offshore  has now started  work on  the 400  million (pounds
sterling) contract to design and build the surface production  facility for BP's
Schiehallion  Field. Up to 3,500 jobs  across  Europe  will be created  by  the
contract award. Registrant's subsidiary, Brown & Root, will have responsibility
for project  management, the design  and fabrication of the FPSO's topsides and
for the vessel installation.

         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 April 8, 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:    April 10, 1996                         By: _______________________
                                                       Robert M. Kennedy
                                                       Vice President - Legal





























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                                  EXHIBIT INDEX



Exhibit                                                          Sequentially
Number                          Description                      Numbered Page

  20                            Press Release of
                                April 8, 1996                      5 of 6
                                Incorporated by Reference
































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FOR IMMEDIATE RELEASE                 Contact:       Guy T. Marcus
April 8, 1996                                        Vice President-Inv. Rel.
                                                     (214) 978-2691

     ALLIANCE STARTS ON BP'S 400 MILLION (POUND STERLING) SCHIEHALLION PROJECT

     DALLAS, Texas -- Halliburton Company (NYSE-HAL) announced today an alliance
involving BP,  Halliburton's Brown & Root subsidiary,  Harland and Wolff, Single
Buoy Moorings  (SBM) and Coflexip  Stena  Offshore (CSO) - which has now started
work on  the 400  million  (pounds sterling) contract  to design  and build the 
surface production facility for BP's Schiehallion Field. The facility comprises 
the world's largest new-build Floating Production Storage and Off-loading (FPSO)
vessel.

     The  announcement  follows  the UK  Government  sanctioning  of the West of
Shetlands  oil  find,  giving  the  operator  the  green  light  for  full-scale
development.  Up to 3,500 jobs across  Europe will be created and made secure by
the contract award. Some of the major  fabrication and equipment  contracts have
already been let,  reflecting the "fast-track"  nature of the project.  Known as
the FPSO Alliance, the contract will be managed by an integrated management team
of all the companies involved.

     Brown & Root will have  responsibility for project  management,  the design
and fabrication of the FPSO's topsides and for the vessel installation.  Harland
and Wolff  will  design  and build the  950,000  barrel  capacity  vessel in its
Belfast facility.  SBM will  design and build the turret and  moorings for the
facility  while CSO will design and provide the riser system.

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     Commenting  on the award on behalf of the  Alliance,  Brown & Root  project
director Arthur Barker,  said; "All the companies  participating,  including BP,
are working closely as an integrated team. The arrangement  involves  innovative
risk sharing incentives that bind the team together," he added.

     Brown & Root  McDermott  Fabricators  (BARMAC),  the joint venture  company
between  Brown & Root  and  J. Ray  McDermott, has  won the  20 million (pounds 
sterling)  contract to fabricate  6,300  tonnes  of process  topsides  for  BP  
Schiehallion's floating production vessel. Work on the topsides is scheduled to 
commence in May of  this year at BARMAC's  Ardersier yard.  Completion  of the  
contract is expected in February  1997 when all the process  packages  will be  
delivered  to Belfast for installation  on the FPSO.  Up to 450 jobs at the yard
will be made secure by the contract award.

     BARMAC  will also  undertake a  3 million (pounds sterling) contract from  
Northampton-based Kvaerner  Paladon for the fabrication of separation  packages 
for the FPSO.  Work will commence on the 900 tonne systems  immediately  and is 
expected to be complete by the end of the year.

     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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