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)

                                  JUNE 25, 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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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 June 25, 1998 registrant issued a press release entitled Halliburton
 Stockholders   Approve  Proposals   pertaining,   among  other  things,  to  an
 announcement that at registrant's special meeting of stockholders held June 25,
 1998 in lieu of its annual meeting,  registrant's stockholders approved each of
 the four proposals voted upon at the meeting.

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 June 25, 1998.

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         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:    June 25, 1998             By:
                                      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
                           June 25, 1998
                           Incorporated by Reference

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FOR IMMEDIATE RELEASE               Contact: Guy T. Marcus
June 25, 1998                                V.P.-Investor Relations
                                             (214) 978-2691


         DALLAS, Texas - At Halliburton  Company's (NYSE:HAL) special meeting of
stockholders  today,  held  in  lieu  of  its  annual  meeting,   the  company's
stockholders  approved each of the following  four  proposals  voted upon at the

                  1.  Amendment  to   Halliburton's   restated   certificate  of
                      incorporation to increase the authorized  number of shares
                      of the company from 400 million to 600 million shares.

                  2.  Issuance  of  Halliburton  common  stock  pursuant  to  an
                      agreement  and  plan  of  merger  between  Halliburton and
                      Dresser Industries, Inc. (NYSE:DI).

                  3.  Election  of the ten nominees named in the proxy statement
                      to serve as directors of Halliburton Company.

                  4.  Appointment   of  Arthur   Andersen  LLP  as   independent
                      accountants to examine the financial  statements and books
                      and records of Halliburton for 1998.

         Halliburton said that the company and Dresser are continuing to provide
requested  information to regulatory bodies and expect to complete the merger in
the fall of 1998.

         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.


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