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)

                                   MAY 8, 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 C. Christopher Gaut,
Executive Vice President and Chief Financial Officer of Halliburton signed these
Certifications  on  May  7,  2003.  The  Certifications  were  furnished  to the
Securities and Exchange Commission, as accompanying correspondence in connection
with the Quarterly Report of Halliburton on Form 10-Q for the period ended March
31, 2003 as filed with the Securities and Exchange Commission on May 8, 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

In connection with the Quarterly  Report of Halliburton  Company (the "Company")
on Form 10-Q for the period  ending March 31, 2003 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, pursuant to 18 U.S.C. ss. 1350,
as adopted pursuant to ss. 906 of the Sarbanes-Oxley Act of 2002, 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
             May 7, 2003



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


In connection with the Quarterly  Report of Halliburton  Company (the "Company")
on Form 10-Q for the period  ending March 31, 2003 as filed with the  Securities
and Exchange  Commission on the date hereof (the  "Report"),  I, C.  Christopher
Gaut, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. ss.
1350, as adopted pursuant to ss. 906 of the Sarbanes-Oxley Act of 2002, 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/ C. Christopher Gaut
             ------------------------------------
             C. Christopher Gaut
             Chief Financial Officer
             May 7, 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:     May 8, 2003                  By: /s/ Margaret E. Carriere
                                          -----------------------------
                                               Margaret E. Carriere
                                               Vice President and Secretary