
                       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, 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 May 8, 1998 registrant  issued a press release entitled  Halliburton
 and Dresser  Announce Special Meetings  pertaining,  among other things,  to an
 announcement that registrant and Dresser Industries, Inc. ("Dresser") have both
 set  May  15,  1998  at the  close  of  business  as the  record  date  for the
 determination  of  shareholders  entitled  to  notice  of and to vote at  their
 respective  special  meetings  of  shareholders  which will be held on June 25,
 1998. The meetings will be held to consider and vote on issues  relating to the
 proposed merger of registrant and Dresser.

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 May 8, 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:    May 8, 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 6
                           May 8, 1998
                           Incorporated by Reference





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