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)

                                DECEMBER 28, 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  December  28,  1998  registrant  issued  a press  release  entitled
Halliburton Items Affecting 1998 Fourth Quarter pertaining,  among other things,
to an  announcement  that  registrant  plans to take a $35  million  pretax ($24
million after tax or $.05 per diluted  share)  special charge in the 1998 fourth
quarter to provide for a reduction of an  additional  2,750  employees  from its
Energy  Services Group business  segment.  Although the quarter has not yet been
completed,  registrant  expects to earn about $.14 to $.16 per diluted  share in
the 1998 fourth 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 December 28, 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:    January 7, 1999             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
                           December 28, 1998
                           Incorporated by Reference







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FOR IMMEDIATE RELEASE           Contact: Guy T. Marcus
December 28, 1998                        Vice President-Investor Relations
                                         (214) 978-2691


                 HALLIBURTON ITEMS AFFECTING 1998 FOURTH QUARTER

         DALLAS, Texas -- Halliburton Company (NYSE:HAL) today announced that it
plans to take a $35 million  pretax ($24 million  after tax or $ .05 per diluted
share)  special  charge in the 1998 fourth quarter to provide for a reduction of
an additional  2,750 employees from its Energy Services Group business  segment.
This employment reduction is in response to the business impact of low crude oil
prices and oil company customers' plans to sharply reduce spending in 1999.

         A number of  customers,  for whom the company is working on projects in
the North Sea, North Africa and Latin America,  have been negatively impacted by
the current low oil price market environment.  As a result, these customers have
restricted  their capital  spending and they have recently placed  extraordinary
pressure on the project claims resolution  process and are now rejecting some of
the company's  claims for  additional  cost incurred by the company.  This is in
stark  contrast  to  more  favorable  negotiating  strategies  employed  by such
customers only months ago which might have resulted in more equitable resolution
to these types of claims.  The same economic  pressures  have more  dramatically
impacted some of the company's joint venture  partners and major  subcontractors
in several of these  projects.  Their  inability to maintain  their share of the
contractual cost, schedule and financial obligations of such projects has placed
additional  financial  burdens on the company.  These pressures have become more
acute in the 1998 fourth quarter and particularly  affect contracts in the Brown
& Root Energy Service business  unit. Consequently, the  company determined that

                                     -more-


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Halliburton Company                  page 2

in  accordance  with generally  accepted accounting principles,  it will provide
$60 million pretax for project losses in the 1998 fourth quarter.

         Although  the quarter  has not yet been  completed,  after  taking into
account the personnel  reduction  special charges and recognizing costs relating
to the project losses,  Halliburton now expects to earn about $ .14 to $ .16 per
diluted share in the 1998 fourth quarter.

         Halliburton  Company,  founded in 1919, is the world's largest provider
of products and services to the  petroleum  and energy  industries.  The company
serves its  customers  with a broad range of products and  services  through its
Energy Services Group, Engineering and Construction Group, and Dresser Equipment
Group business segments. In 1997 Halliburton conducted business with a workforce
of  approximately  100,000 in over 120 countries.  The company's  World Wide Web
site can be accessed at http://www.halliburton.com.

         NOTE:  In  accordance  with the Safe Harbor  provisions  of the Private
Securities  Litigation  Reform Act of 1995,  Halliburton  Company  cautions that
statements  in this press  release  which are forward  looking and which provide
other than  historical  information,  involve risks and  uncertainties  that may
impact the company's actual results of operations. Please see Halliburton's Form
10-Q for the quarter ended September 30, 1998 for a more complete  discussion of
such risk factors.

                                       ###

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