

                       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)

                                  JULY 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 July 22, 1998 registrant issued a press release entitled Halliburton
 1998 Second Quarter Net Income Up 34 Percent pertaining, among other things, to
 an  announcement  that  registrant's  1998 second  quarter net income of $136.5
 million  increased  34 percent  compared to $101.9  million  earned in the 1997
 second quarter. Registrant's consolidated revenues were $2,475.6 million in the
 1998 second quarter, an increase of 11 percent over last year's second quarter.
 For the six month period ended June 30, 1998,  net income  increased 38 percent
 to $254.3 million while revenues were 17 percent higher than the 1997 six month
 period.

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 July 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:    July 23, 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 7
                           July 22, 1998
                           Incorporated by Reference





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