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 21, 1999

                               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  April  21,  1999  registrant   issued  a  press  release   entitled
Halliburton's  Brown & Root Services Provides Logistics Services to Support U.S.
Forces in Albania  pertaining,  among  other  things,  to an  announcement  that
registrant's Brown & Root Services business unit is providing  logistics support
services to U.S. Army soldiers being deployed for operations in Albania.

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 21, 1999.

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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:    April 27, 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
                           April 21, 1999
                           Incorporated by Reference

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FOR IMMEDIATE RELEASE                  CONTACT: Wendy Hall Nantz
April 21, 1999                                  Public Relations
                                                Halliburton Company
                                                (713) 676-5227


DALLAS,  Texas - Brown & Root Services  (BRS),  a business  unit of  Halliburton
Company  (NYSE:  HAL),  is providing  logistics  support  services to U.S.  Army
soldiers being deployed for operations in Albania.
         The work is being performed under a contract  previously awarded by the
Transatlantic Programs Center to Brown & Root Services, based in Houston, Texas.
Under  the  existing  contract,  logistics  services  - such  as  life  support,
transportation,  and  maintenance - are provided for  contingency or sustainment
operations that support U.S. Army Europe in the Balkans.
          "We are proud to support the U.S. troops in Albania," said Dave Lesar,
president and chief operating officer, Halliburton Company.  "Our support to the
deployed  U.S. military  force has  offered a  significant  cost  savings to the
government,  and  we  plan to  continue  to provide  complete and cost effective
service for this critical mission."
         In support of U.S. Forces, Brown & Root Services will provide temporary
housing   (tent   complexes),    food   services,   parking   and   road   work,
waste/trash/vector control, power generation, airhead operations, transportation
services and mail  delivery.  Brown & Root Services was tasked to begin planning
for the camp on April 5, 1999.

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         Brown &  Root Services  is currently   performing  similar  services in
Hungary,  Croatia,  Bosnia and  Macedonia in support of  Operation Joint  Forge,
which  supports  peacekeeping  efforts  in  Bosnia.  Brown & Root  Services  has
provided logistics services to the Army since 1992. It has provided  engineering
and logistics services to the troops in the Balkans region, since late 1995.
         "Our  experience  in the Balkans has prepared us for this  assignment,"
said  Randy  Harl,  president,  Brown  & Root  Services.  "We are  proud  of our
accomplishments  and plan to  provide  the same  high  level  of  service  while
supporting the troops in Albania."
         Brown & Root Services,  one of America's top federal  contractors,  was
selected by the United States Army as the "Public Works  Contractor of the Year"
for its work at Fort Benning, Georgia. Brown & Root Services provides "Lifecycle
Management"  for global  government and private  clients.  Lifecycle  Management
consists of the master planning, design, construction,  operations, maintenance,
investment  management and decommissioning of facilities.  Brown & Root Services
is a business unit of Halliburton Company, headquartered in Dallas, Texas.
         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.  The company's  World Wide Web site can be accessed at


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