

                       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)

                                NOVEMBER 24, 1998

                               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.

         In  connection  with the  offering,  sale and delivery by Registrant of
$150 million  principal  amount  Registrant's  5 5/8% Notes due December 1, 2008
(the "Notes") on November 24, 1998,  Registrant  is filing  herewith as exhibits
the final copy of the Terms  Agreement and the form of Note. The offering,  sale
and delivery of the Notes,  which constitute a part of Registrant's  Medium Term
Notes Due Nine Months or More From Date of Issue, Series A, have been registered
pursuant  to the  registration  provisions  of the  Securities  Act of 1933,  as
amended, by virtue of Registrant's  Registration Statement on Form S-3 (File No.
33-65772) which, as amended by Post-effective  Amendment No. 2, became effective
on December 19, 1996.

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 1.1 - Terms  Agreement dated November 19, 1998 between
                  Halliburton Company and Merrill Lynch, Pierce,  Fenner & Smith
                  Incorporated and the other agents signatory thereto.

                  Exhibit 4.1 - Form of Note.




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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:  December 18, 1998                  By: /s/ Susan S. Keith
                                                ---------------------------
                                                  Susan S. Keith
                                                  Vice President, Secretary and
                                                  Corporate Counsel




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                                  EXHIBIT INDEX


Exhibit                                                       Sequentially
Number                     Description                        Numbered Page

1.1                        Terms Agreement                    5 of 27

4.1                        Form of Note                       16 of 27







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