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)

                                   MAY 6, 1996

                               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. 73-0271280

                               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 May 6, 1996,  registrant issued a press release entitled Halliburton
Installs   World's  First   Multi-Lateral   System  With  Full  Re-Entry  Access
pertaining, among other things, to an announcement that registrant's Halliburton
Energy  Services  business  segment has  successfully  installed a multi-lateral
system with full lateral liner connectivity,  a  hydraulically-isolated  lateral
junction and full-bore lateral re-entry access.  The system is the world's first
to provide  full-bore  re-entry  access to the  lateral  while  maintaining  the
integrity of the main wellbore.  The multi-lateral system was installed in Norsk
Hydro's Oseberg field. The successful installation of this system is viewed as a
technical breakthrough by Norsk Hydro and registrant.

         The foregoing  summary is subject to the full text of the press release
with respect  thereto,  a copy of which is attached  hereto as Exhibit 20, which
exhibit is incorporated herein by reference.

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 May 6, 1996
                  ----------











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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:    May 6, 1996                                 By: _______________________
                                                         Robert M. Kennedy
                                                         Vice President - Legal





























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                                  EXHIBIT INDEX



Exhibit                                                            Sequentially
Number                     Description                             Numbered Page
- -------                    -----------                             -------------
  20                       Press Release of
                           May 6, 1996                                5 of 7
                           Incorporated by Reference






























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FOR IMMEDIATE RELEASE          
- ---------------------                  Contact  - Guy T. Marcus
May 6, 1996                                       Vice President-Inv. Rel.
                                                  (214) 978-2691


HALLIBURTON INSTALLS WORLD'S FIRST MULTI-LATERAL SYSTEM WITH FULL
                    RE-ENTRY ACCESS
- -----------------------------------------------------------------

     DALLAS, Texas -- Halliburton Company's (NYSE-HAL) Halliburton Energy
Services business segment announced today that it has successfully installed a
multi-lateral system with full lateral liner connectivity, a hydraulically-
isolated lateral junction and full-bore lateral re-entry access.  The system, 
installed for Norwegian operator Norsk Hydro, is the world's first to provide 
full-bore re-entry access to the lateral while maintaining the integrity of the
main wellbore.

     The multi-lateral system was installed in Norsk Hydro's Oseberg field,
located approximately 120 kilometers west of Bergen in the Norwegian North Sea.
The Oseberg C platform was installed in 1988 to drain the northern portion of
the field. Norsk Hydro set a specific goal for increasing recoverable reserves
from this field. Multi-lateral technology was identified as a means to help
achieve the goal.

     The multi-lateral system needed the capability to commingle production from
primary and secondary formations. Due to pressure differentials, each formation
would also need to be isolated at various times. Additionally, the secondary


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Halliburton Company

formation would likely require re-perforation during its production life, so
selective re-entry to the main and secondary wellbores for running perforating
guns, production logs and installing production control devices was a required
feature.

     Halliburton's Multi-Lateral System 3000(TM)was chosen for the application
because of its full-bore access which provides flexibility in running downhole
tools, and lateral isolation which enhances pressure integrity and increases
production control.

     Johan Mikkelsen, assistant director in Hydro's Exploration and Production
Division said, "This multi-lateral system will allow us to increase recoverable
reserves economically. The ability to avoid drilling additional wells while
maintaining re-entry access to the lateral is very beneficial."

     Halliburton has drilled and completed hundreds of multi- lateral wells
including duals and quads with separated production. The Norsk Hydro well
incorporates connectivity, isolation and access in a single system. The system
uses 9 5/8- in. casing with a 7-in. steel liner connected mechanically and
isolated at the junction with Halliburton's M-Seal high-impact sealant. A 7-in.
production tubing string is installed enabling maximum flow in a monobore
configuration and full-bore re-entry access to the lateral.

     Norsk Hydro and Halliburton worked closely throughout the planning,
development and execution phases of the project. The successful installation of

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Halliburton Company

this system is viewed as a technical breakthrough by both companies, providing a
new opportunity for innovative production schemes and a potential change in the
use of surface facilities.

     "Using this technology, Hydro will produce considerably more oil in certain
fields, at far lower prices than in the past." "This is a milestone for us,"
added Mikkelsen.

     As a fully integrated technical solution, System 3000 combines
Halliburton's project design and management, directional drilling, reservoir
description, cementing, and completion capabilities.

     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.

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