
                       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)

                                 APRIL 20, 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.

         On  April  20,  1998  registrant   issued  a  press  release   entitled
 Halliburton and Dresser Receive  Information  Request  pertaining,  among other
 things,  to an announcement that registrant and Dresser  Industries,  Inc. have
 received requests for additional  information concerning the proposed merger of
 registrant  and Dresser from the Antitrust  Division of the U.S.  Department of
 Justice.  The companies indicated that the requests for additional  information
 were not  unexpected  and they plan to respond  promptly to the  Department  of
 Justice.

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 April 20, 1998.




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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:    April 22, 1998                   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
                           April 20, 1998
                           Incorporated by Reference





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