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)

                                 MARCH 28, 2003

                               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


                               4100 Clinton Drive
                            Houston, Texas 77020-6299
                    (Address of principal executive offices)

                         Registrant's telephone number,
                       including area code - 713-676-3011



         INFORMATION TO BE INCLUDED IN REPORT

Item 9.  Regulation FD Disclosure

         Halliburton   Company   (Halliburton)   is   furnishing   herewith  the
Certifications pursuant to 18 U.S.C. Section 1350 as adopted pursuant to Section
906 of the  Sarbanes-Oxley  Act of 2002. David J. Lesar,  Chairman of the Board,
President,  and Chief Executive  Officer of Halliburton,  and Douglas L. Foshee,
Executive Vice President and Chief Financial Officer of Halliburton signed these
Certifications  on March 25,  2003.  The  Certifications  were  furnished to the
Securities and Exchange Commission, as accompanying correspondence in connection
with the Annual Report of Halliburton on Form 10-K for the period ended December
31, 2002 as filed with the Securities and Exchange Commission on March 28, 2003.

         The text of these Certifications is as follows:


                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


This  certification is provided pursuant to ss. 906 of the Sarbanes-Oxley Act of
2002, 18 U.S.C. ss. 1350, and accompanies the Annual Report on Form 10-K for the
period ended December 31, 2002 of Halliburton  Company (the  "Company") as filed
with the Securities and Exchange Commission on the date hereof (the "Report").

I, David J. Lesar, Chief Executive Officer of the Company, certify that:

         (1)    The Report fully complies with the requirements of section 13(a)
                or 15(d) of the Securities Act of 1934; and

         (2)    The information  contained in the Report fairly presents, in all
                material  respects,  the  financial  condition  and  results  of
                operations of the Company.



/s/ David J. Lesar
-----------------------
David J. Lesar
Chief Executive Officer
March 25, 2003



                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



This  certification is provided pursuant to ss. 906 of the Sarbanes-Oxley Act of
2002, 18 U.S.C. ss. 1350, and accompanies the Annual Report on Form 10-K for the
period ended December 31, 2002 of Halliburton  Company (the  "Company") as filed
with the Securities and Exchange Commission on the date hereof (the "Report").

I, Douglas L. Foshee, Chief Financial Officer of the Company, certify that:

         (3)    The Report fully complies with the requirements of section 13(a)
                or 15(d) of the Securities Act of 1934; and

         (4)    The information  contained in the Report fairly presents, in all
                material  respects,  the  financial  condition  and  results  of
                operations of the Company.



/s/ Douglas L. Foshee
------------------------
Douglas L. Foshee
Chief Financial Officer
March 25, 2003



                                   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:     March 28, 2003               By: /s/ Margaret E. Carriere
                                          ----------------------------------
                                               Margaret E. Carriere
                                               Vice President and Secretary