
                       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)

                                  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






                                Page 1 of 5 Pages
                       The Exhibit Index Appears on Page 4
<PAGE>

         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 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.







                                Page 2 of 5 Pages
                       The Exhibit Index Appears on Page 4

<PAGE>

                                   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:    June 25, 1998             By:
                                      --------------------------------
                                      Susan S. Keith
                                      Vice President and Secretary






                                Page 3 of 5 Pages
                       The Exhibit Index Appears on Page 4
<PAGE>

                                  EXHIBIT INDEX


Exhibit                                                       Sequentially
Number                     Description                        Numbered Page

20                         Press Release of                   5 of 5
                           June 25, 1998
                           Incorporated by Reference








                                Page 4 of 5 Pages
                       The Exhibit Index Appears on Page 4

