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)

                                 MARCH 31, 2000

                               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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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  March  27,  2000  registrant   issued  a  press  release   entitled
"Halliburton's New Management  Assignments,"  pertaining to, among other things,
the announcement by registrant of new management leadership  assignments for the
Energy Services Group,  its Halliburton  Energy Services and Brown & Root Energy
Services business units and the Brown & Root Services business unit.

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 March 31, 2000.

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         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:    March 31, 2000                 By: /s/ Susan S. Keith
                                                Susan S. Keith
                                                Vice President and Secretary

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                                  EXHIBIT INDEX

Exhibit                                                        Sequentially
Number                     Description                         Numbered Page

20                         Press Release of                    5 of 6
                           March 31, 2000
                           Incorporated by Reference

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FOR IMMEDIATE RELEASE                        Contact: Guy T. Marcus
03/31/00                                     Vice President-Investor Relations


         DALLAS,  Texas -- Halliburton  Company  (NYSE:HAL)  announced today new
management  leadership  assignments designed to better facilitate the increasing
upstream  petroleum  industry  needs  for  integrated   solutions  and  services
capabilities  that exist within the company's  Energy  Services  Group  business
segment -- and the segment's  Halliburton  Energy Services,  Brown & Root Energy
Services and Landmark Graphics Corporation business units.
         The new  assignments,  which  become  effective  April 3, 2000,  are as
o             Energy Services Group - Edgar Ortiz (58) will become president and
              chief  executive  officer of the Energy  Services  Group  business
              segment,  which consists of Halliburton  Energy Services,  Brown &
              Root Energy  Services and Landmark  Graphics.  Ortiz will have the
              direct  responsibility for the group and will develop the strategy
              and vision that will enable us to capture the integrated  value of
              these companies.  Ortiz has an excellent track record in a variety
              of  management  positions in his 22 years with the  company,  most
              recently as president of Halliburton Energy Services.
o             Brown  & Root  Energy  Services  - Randy  Harl  (49)  will  become
              president of Brown & Root Energy Services.  Harl has most recently
              done an  excellent  job in managing  the  profitable  Brown & Root
              Services  business  unit.  He brings  to the  Brown & Root  Energy
              Services  job  25  years  of  experience  in the  engineering  and
              construction business.

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         Halliburton Company                         page 2

o             Halliburton  Energy  Services  -  Jody  Powers  (53)  will  become
              president  of  Halliburton  Energy  Services.  Powers  has a long,
              successful  track record of 31 years at Halliburton in a number of
              senior  management  positions.  He has spent the last three  years
              building and managing our successful  strategic account management
o             Brown & Root  Services - Larry Pope (58) will become  president of
              Brown & Root  Services.  Pope has spent his  entire  career in the
              engineering and construction industry, including the last 12 years
              at  Halliburton.  He has been  president  of Brown & Root and most
              recently chief operating officer of Kellogg Brown & Root.
         Dick  Cheney,  Halliburton  Company's  chairman  of the board and chief
executive officer,  said, "The new assignments will place management  leadership
skills  within  the  organization  to  better  facilitate   achievement  of  our
objectives to improve  operational  efficiencies,  take advantage of cost-saving
opportunities,   speed  the  decision   making   process  and   strengthen   the
organization's  position as we prepare to take  advantage  of market  conditions
that are now beginning to improve worldwide."
         Halliburton  Company,  founded in 1919, is the world's largest provider
of products and services to the  petroleum  and energy  industries.  The company
serves its  customers  with a broad range of products and  services  through its
Energy Services Group,  Engineering and Construction Group and Dresser Equipment
Group business  segments.  The company's  World Wide Web site can be accessed at

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