FOR IMMEDIATE RELEASE                        Contact - Guy T. Marcus
July 20, 1995                                          Vice President-Inv. Rel.
                                                       (214) 978-2691

          HALLIBURTON CALLS CONVERTIBLE DEBENTURES

     DALLAS,  Texas -- Halliburton  Company (NYSE - HAL) announced today that it
is calling the entire outstanding  principal amount of the company's zero coupon
convertible  subordinated  debentures due March 13, 2006 (the  "Debentures")  on
September  1,  1995  (the  "Redemption  Date").  The  redemption  price  will be
$536.5029  per  $1,000.00  principal  amount  of  Debentures  at  maturity.  The
redemption price represents the original issue price plus accrued original issue
discount to the Redemption Date.

     The total cost of the redemption, assuming all Debentures are submitted for
redemption, will be approximately $391 million.

Halliburton   will  fund  the  redemption   primarily  with  cash  reserves  and
secondarily with short term borrowings.

     Payment of the Debentures  called for  redemption  will be made on or after
the Redemption Date upon  presentation and surrender of the Debentures at one of
the following principal corporate trust offices of the Trustee as follows -

BY MAIL

Texas Commerce Bank N.A.
Attn - Corporate Trust Operations
       Div/Bond Call Unit
P.O. Box 2320
Dallas, Texas 75221-2320


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BY OVERNIGHT DELIVERY OR HAND

Texas Commerce Bank N.A.     Texas Commerce Trust Company
Registered Bond Events       80 Broad Street, 4th Floor
1900 Pacific, 16th Floor     New York, NY 10004
Dallas, Texas 75201          Attn: Barbara Telford

     At the option of the  debentureholder,  any Debenture may be converted into
Halliburton  Company  common  stock at the  conversion  rate of 6.824 shares per
$1,000.00  principal  amount of  Debentures  at  maturity  at any time until and
including, but not after, the close of business on August 14, 1995 at which time
the option will  terminate.  Holders who elect to convert  will  receive cash in
lieu of  fractional  shares.  In order to  exercise  the  conversion  privilege,
debentureholders  must  surrender  such  Debentures to the Trustee at one of the
above  addresses,  together  with the  executed  conversion  notice  in the form
provided on the  Debentures  accompanied  by the proper  assignments  thereof in
blank, no later than the close of business on August 14, 1995.

     Debentureholders seeking additional information regarding
the redemption or conversion of the Debentures may telephone
Texas Commerce Bank N. A.  at (800) 275-2048.

     Halliburton  Company  is one  of the  world's  largest  diversified  energy
services, engineering, maintenance, and construction companies. Founded in 1919,
Halliburton  provides a broad range of energy services and products,  industrial
and marine  engineering  and  construction  services,  and property and casualty
insurance services.

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