

                       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 22, 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  22,  1998  registrant   issued  a  press  release   entitled
 Halliburton 1998 First Quarter Net Income Up 42 Percent pertaining, among other
 things,  to an  announcement  of its 1998  first  quarter  net income of $117.8
 million ($.44 per share  diluted),  an increase of 42 percent  compared to 1997
 first  quarter  net  income  of  $83.0   million  ($.32  per  share   diluted).
 Registrant's  1998  consolidated  revenues for the first  quarter  increased 24
 percent to $2.4 billion, compared to the year earlier quarter.

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 22, 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 8
                           April 22, 1998
                           Incorporated by Reference



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