FOR IMMEDIATE RELEASE               Contact:  Cedric Burgher
- ---------------------                         Vice President, Investor Relations
June 4, 2002                                  713-676-4608

                                              Wendy Hall
                                              Manager, Media Relations
                                              713-676-5227


HALLIBURTON ASBESTOS PLAINTIFFS AGREE TO EXTEND CURRENT STAY ON ASBESTOS CLAIMS

Dallas,  Texas - Halliburton  Company  (NYSE:  HAL) today  announced that it has
reached  agreement with  Harbison-Walker  Refractories  Company and the Official
Committee  of  Asbestos   Creditors  in  the   Harbison-Walker   bankruptcy   to
consensually  extend the period of the stay contained in the Bankruptcy  Court's
temporary restraining order until July 16, 2002. The Committee also informed the
court that further  30-day  extensions are  anticipated as long as  negotiations
proceed in a constructive manner. The Court's temporary restraining order, which
was  originally  entered on February 14, 2002,  stays more than 200,000  pending
asbestos claims against  Halliburton's  subsidiary Dresser Industries,  Inc. For
more  details on the stay  entered by the Court on February  14, and extended on
February 21 and April 4, Halliburton refers to its earlier press releases of May
20, 2002, February 22, 2002 and February 14, 2002.

Halliburton,  founded  in  1919,  is one of the  world's  largest  providers  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 and Engineering and  Construction  Group business  segments.  The
company's World Wide Web site can be accessed at www.halliburton.com.



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