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)

                                  JUNE 4, 2002

                               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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         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 June 4, 2002 registrant issued a press release entitled "Halliburton
Asbestos Plaintiffs Agree to Extend Current Stay on Asbestos Claims," pertaining
to an announcement  that registrant has reached  agreement with  Harbison-Walker
Refractories  Company and the Official  Committee  of Asbestos  Creditors in the
Harbison-Walker  bankruptcy  to  consensually  extend  the  period  of the  stay
contained in the Bankruptcy  Court's temporary  restraining order until July 16,
2002. The Committee  also informed the Court that further 30-day  extensions are
anticipated  as long as  negotiations  proceed  in a  constructive  manner.  The
Court's  temporary  restraining  order  originally  entered on February 14, 2002
stays more than 200,000 pending asbestos claims against registrant's subsidiary,
Dresser  Industries,  Inc. See  registrant's  earlier press  releases of May 20,
2002,  February  22, 2002 and  February  14,  2002 for more  details on the stay
entered by the Court on February  14, 2002 and extended on February 21 and April
4, 2002.


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 June 4, 2002.







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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:  June 4, 2002                     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 5
                           June 4, 2002
                           Incorporated by Reference







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