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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FOR IMMEDIATE RELEASE   Contact: Guy T. Marcus          George H. Juetten
May 8, 1998                      Halliburton Company    Dresser Industries
                                 (214) 978-2691         (214) 740-6757

                HALLIBURTON AND DRESSER ANNOUNCE SPECIAL MEETINGS

         DALLAS, Texas -- Halliburton Company (NYSE:HAL) and Dresser Industries,
Inc. (NYSE:DI) jointly announce that both companies' board of directors have 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
Halliburton and Dresser.
         Both companies will hold their special meetings of shareholders on June
25, 1998 in Dallas, Texas.  Halliburton Company's shareholders will consider and
vote on proposals to increase the  company's  authorized  shares of common stock
from 400 million to 600 million shares and approve issuance of approximately 175
million shares of Halliburton common stock pursuant to the previously  announced
merger agreement with Dresser. Halliburton's shareholders will also consider and
vote  upon  items  normally   addressed  at  the  company's  annual  meeting  of
shareholders,  which was postponed  from its  originally  scheduled May 19, 1998
date so that such items could be combined with items  associated with the merger
at a single meeting of shareholders.  Dresser  Industries,  Inc.'s  shareholders
will consider and vote on the proposed merger with  Halliburton at their special
meeting of shareholders.

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         Halliburton  Company is one of the world's largest  diversified  energy
services, engineering, maintenance, and construction companies. Founded in 1919,
Halliburton  provides a broad range of energy services and products,  industrial
and marine engineering and construction services.
         Dresser is a leading global  supplier to the total  hydrocarbon  energy
stream. Dresser's product and service offerings encompass sophisticated drilling
and well construction systems as well as technologies, engineering equipment and
project management for the transportation and conversion of oil and natural gas.

                                       ###


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