<PAGE>
 
    AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON OCTOBER 6, 1998
                                                     Registration No. 333-
================================================================================

                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549

                               -----------------


                                   FORM S-8
                            REGISTRATION STATEMENT
                                     UNDER
                          THE SECURITIES ACT OF 1933

                               -----------------

                              HALLIBURTON COMPANY
            (Exact name of registrant as specified in its charter)

          DELAWARE                                         75-2677995
(State or other jurisdiction of                         (I.R.S. Employer
incorporation or organization)                         Identification No.)

                              3600 LINCOLN PLAZA
                            500 NORTH AKARD STREET
                           DALLAS, TEXAS  75201-3391
         (Address of principal executive offices, including zip code)

                               -----------------

               DRESSER INDUSTRIES, INC. 1982 STOCK OPTION PLAN*

        DRESSER INDUSTRIES, INC. 1989 RESTRICTED INCENTIVE STOCK PLAN*

            DRESSER INDUSTRIES, INC. 1992 STOCK COMPENSATION PLAN*

STOCK OPTIONS GRANTED BY DRESSER INDUSTRIES, INC. TO THE FOLLOWING FORMER NON-
                              EMPLOYEE DIRECTORS:
SAMUEL B. CASEY, JR., LAWRENCE S. EAGLEBURGER, SYLVIA A. EARLE, RAWLES FULGHAM,
JOHN A. GAVIN, RAY L. HUNT, J. LANDIS MARTIN, LIONEL H. OLMER, JAY A. PRECOURT, 
                              RICHARD W. VIESER*

              DRESSER INDUSTRIES, INC. DEFERRED COMPENSATION PLAN
                         FOR NON-EMPLOYEE DIRECTORS/+/

            DRESSER INDUSTRIES, INC. DEFERRED COMPENSATION PLAN/+/

         BAROID CORPORATION 1990 LONG TERM PERFORMANCE INCENTIVE PLAN*

     WHEATLEY TXT CORPORATION 1990 AMENDED AND RESTATED STOCK OPTION PLAN*

                           (Full title of the plans)

                               -----------------

                                                        Copy to:
              LESTER L. COLEMAN
 EXECUTIVE VICE PRESIDENT AND GENERAL COUNSEL      WILLIAM E. JOOR III
             HALLIBURTON COMPANY                 VINSON & ELKINS L.L.P.
              3600 LINCOLN PLAZA                   1001 FANNIN STREET
            500 NORTH AKARD STREET                2300 FIRST CITY TOWER
          DALLAS, TEXAS  75201-3391             HOUSTON, TEXAS 77002-6760
   (Name and address of agent for service)

                                (214) 978-2600
         (Telephone number, including area code, of agent for service)

                        CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
===================================================================================================================
 Title of securities        Amount to be           Proposed maximum          Proposed maximum         Amount of
   to be registered          registered        offering price per share  aggregate offering price  registration fee
-------------------------------------------------------------------------------------------------------------------
<S>                     <C>                    <C>                       <C>                       <C>
Common Stock,           4,023,450 shares/(2)/         $34.20/(4)/         $137,601,990/(4)/
$2.50 par value/(1)/    3,300,000 shares/(3)/         $27.84375/(5)/      $ 91,884,375/(5)/         $67,699 
===================================================================================================================
</TABLE>
(1)  This Registration Statement also pertains to rights to purchase shares of
     Series A Junior Participating Preferred Stock of the Registrant. One right
     is attached to and trades with each share of Common Stock. Until the
     occurrence of certain events, the rights are not exercisable and will not
     be evidenced or transferred a part from the Common Stock. Any value
     attributable to such rights is reflected in the market price of the Common
     Stock.
(2)  Number of shares registered that may be issued pursuant to the Plans
     identified by an "*."
(3)  Number of shares registered that may be issued pursuant to the Plans
     identified by an "+."
(4)  Estimated, solely for purposes of calculating the registration fee, in
     accordance with Rule 457(h), based upon the weighted average exercise price
     of the options granted pursuant to the Plans described in Note 1 above.
(5)  Estimated solely for purposes of calculating the registration fee, in
     accordance with Rule 457(h), on the basis of the price of securities of the
     same class, as determined in accordance with Rule 457(c), using the average
     of the high and low prices reported on the New York Stock Exchange for the
     Common Stock on October 2, 1998. 

================================================================================
<PAGE>
 
                                    PART II
              INFORMATION REQUIRED IN THE REGISTRATION STATEMENT


ITEM 3.   INCORPORATION OF DOCUMENTS BY REFERENCE.

     The following documents, which have been filed with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Exchange Act
of 1934, as amended (the "Exchange Act"), by Halliburton Company (Exchange Act
Registration No. 1-03492), a Delaware corporation (the "Registrant"), are
incorporated herein by reference and made a part hereof:

          (a)  Annual Report on Form 10-K for the fiscal year ended December
               31, 1997;

          (b)  Quarterly Reports on Form 10-Q for the quarters ended March 31,
               1998 and June 30, 1998;

          (c)  Current Reports on Form 8-K filed with the Commission on January
               2, 1998; January 28, 1998; February 2, 1998; February 20, 1998;
               March 2, 1998; March 24, 1998; April 23, 1998; April 23, 1998;
               May 13, 1998; May 20, 1998; June 2, 1998; June 25, 1998; June 25,
               1998; July 9, 1998; July 16, 1998; July 16, 1998; July 21, 1998;
               July 24, 1998; July 24, 1998; August 24, 1998; September 1, 1998;
               and October 5, 1998.

          (d)  The description of the Common Stock contained in the Registration
               Statement on Form 8-B filed with the Commission on December 12,
               1996.

     All documents filed by the Registrant pursuant to Sections 13(a), 13(c), 14
and 15(d) of the Exchange Act subsequent to the effective date of this
Registration Statement, prior to the filing of a post-effective amendment to
this Registration Statement indicating that all securities offered hereby have
been sold or deregistering all securities then remaining unsold, shall be deemed
to be incorporated by reference herein and to be a part hereof from the date of
filing of such documents.  Any statement contained herein or in any document
incorporated or deemed to be incorporated by reference herein shall be deemed to
be modified or superseded for purposes of this Registration Statement to the
extent that a statement contained herein or in any other subsequently filed
document which also is or is deemed to be incorporated by reference herein
modifies or supersedes such statement.  Any such statement so modified or
superseded shall not be deemed to constitute a part of this Registration
Statement, except as so modified or superseded.

     The consolidated financial statements included in the Registrant's Annual
Reports on Form 10-K incorporated herein by reference have been audited by
Arthur Andersen LLP, independent public accountants, as indicated in their
reports with respect thereto, and are included herein in reliance upon the
authority of said firm as experts in accounting and auditing in giving said
reports.

ITEM 4.   DESCRIPTION OF SECURITIES.

     Not applicable.

ITEM 5.   INTERESTS OF NAMED EXPERTS AND COUNSEL.

     None.

ITEM 6.   INDEMNIFICATION OF DIRECTORS AND OFFICERS.

     Under Section 145 of the General Corporation Law of the State of Delaware
(the "DGCL"), a Delaware corporation has the power, under specified
circumstances, to indemnify its directors, officers, employees and agents in
connection with threatened, pending or completed actions, suits or proceedings,
whether civil, criminal, administrative or investigative (other than an action
by or in right of the corporation), brought against them by reason of the fact
that they were or are such directors, officers, employees or agents, against
expenses, judgments, fines and amounts paid in settlement actually and
reasonably incurred in any such action, suit or proceeding. Article X of the
Registrant's Restated Certificate of Incorporation together with Section 39 of
its By-Laws provide for indemnification of each person who is or was made a
party to any actual or threatened civil, criminal, administrative or
investigative action, suit or proceeding because such person is or was an
officer or director of the Registrant or is a person who is or was serving

                                      -2-
<PAGE>
 
at the request of the Registrant as a director, officer, employee or agent of
another corporation or of a partnership, joint venture trust or other
enterprise, including service relating to employee benefit plans, to the fullest
extent permitted by the DGCL as it existed at the time the indemnification
provisions of the Registrant's Restated Certificate of Incorporation and By-Laws
were adopted or as may be thereafter amended. Section 39 of the Registrant's By-
Laws and Article X of its Restated Certificate of Incorporation expressly
provide that they are not the exclusive methods of indemnification.

     Section 39 of the By-Laws provides that the Registrant may maintain
insurance, at its own expense, to protect itself and any director, officer,
employee or agent of the Registrant or of any other entity against any expense,
liability or loss, regardless of whether the Registrant would have the power to
indemnify such person against such expense, liability or loss under the DGCL.

     Section 102(b)(7) of the DGCL provides that a certificate of incorporation
may contain a provision eliminating or limiting the personal liability of a
director to the corporation or its stockholders for monetary damages for breach
of fiduciary duty as a director, provided that such provision shall not
eliminate or limit the liability of a director (i) for any breach of the
director's duty of loyalty to the corporation or its stockholders, (ii) for acts
or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (iii) under Section 174 of the DGCL (relating to
liability for unauthorized acquisitions or redemptions of, or dividends on,
capital stock) or (iv) for any transaction from which the director derived an
improper personal benefit. Article XV of the Registrant's Restated Certificate
of Incorporation contains such a provision.

ITEM 7.   EXEMPTION FROM REGISTRATION CLAIMED.

     Not applicable.

ITEM 8.   EXHIBITS.

     Unless otherwise indicated below as being incorporated by reference to
another filing of the Registrant with the Commission, each of the following
exhibits is filed herewith:

      4.1 -    Restated Certificate of Incorporation of the Registrant
               (incorporated by reference to Exhibit 3(a) to the Registrant's
               Quarterly Report on Form 10-Q for the quarter ended June 30, 1998
               (Exchange Act Registration No. 1-03492) filed with the Commission
               on August 12, 1998).

      4.2 -    By-Laws, as amended, of the Registrant (incorporated by reference
               to Exhibit 3.2 to the Registrant's Registration Statement on Form
               S-3 (Registration No. 333-32731) filed with the Commission on
               August 1, 1997).

      5.1 -    Opinion of Vinson & Elkins L.L.P. regarding legality.

     23.1 -    Consent of Arthur Andersen L.L.P.

     23.2 -    Consent of Vinson & Elkins L.L.P. (included in Exhibit 5.1).

     24.1 -    Powers of Attorney.

                                 UNDERTAKINGS

     The Registrant hereby undertakes:

     (1)  To file, during any period in which offers or sales are being made, a
post-effective amendment to this Registration Statement:

          (a)  To include any prospectus required by Section 10(a)(3) of the
     Securities Act of 1933, as amended (the "Securities Act");

          (b)  To reflect in the prospectus any facts or events arising after
     the effective date of this Registration Statement (or the most recent post-
     effective amendment thereof) which, individually or in the aggregate,
     represent a fundamental change in the information set forth in this
     Registration Statement;

                                      -3-
<PAGE>
 
          (c)  To include any material information with respect to the plan of
     distribution not previously disclosed in this Registration Statement or any
     material change to such information in this Registration Statement;

provided, however, that paragraphs (1)(a) and (1)(b) do not apply if the
information required to be included in a post-effective amendment by those
paragraphs is contained in periodic reports filed by the Registrant pursuant to
Section 13 or Section 15(d) of the Exchange Act that are incorporated by
reference in this Registration Statement.

     (2)  That, for the purpose of determining any liability under the
Securities Act, each such post-effective amendment shall be deemed to be a new
registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.

     (3)  To remove from registration by means of a post-effective amendment any
of the securities being registered which remain unsold at the termination of the
offering.

     (4)  That, for the purposes of determining any liability under the
Securities Act, each filing of the Registrant's annual report pursuant to
Section 13(a) or Section 15(d) of the Exchange Act (and, where applicable, each
filing of an employee benefit plan's annual report pursuant to Section 15(d) of
the Exchange Act) that is incorporated by reference in this Registration
Statement shall be deemed to be a new registration statement relating to the
securities offered therein, and the offering of such securities at that time
shall be deemed to be the initial bona fide offering thereof.

     (5)  Insofar as indemnification for liabilities arising under the
Securities Act may be permitted to directors, officers and controlling persons
of the Registrant pursuant to the foregoing provisions, or otherwise, the
Registrant has been advised that in the opinion of the Commission such
indemnification is against public policy as expressed in the Securities Act and
is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the Registrant of expenses
incurred or paid by a director, officer or controlling person of the Registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the Registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.

                                      -4-
<PAGE>
 
                                  SIGNATURES

Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Dallas, State of Texas, on the 5th day of October,
1998.

                                      HALLIBURTON COMPANY

                                      By:  /s/ Richard B. Cheney
                                           -------------------------------------
                                           Richard B. Cheney
                                           Chief Executive Officer

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated on the 5th day of October, 1998.

               Signature                                Title
               ---------                                -----

     /s/  Richard B. Cheney               Chief Executive Officer and Director
----------------------------------------  (Principal Executive Officer)
          Richard B. Cheney

     /s/  Gary V. Morris                  Executive Vice President and Chief 
----------------------------------------  Financial Officer (Principal Financial
          Gary V. Morris                  Officer

     /s/  Robert Charles Muchmore, Jr.    Vice President, Controller and 
----------------------------------------  Principal Accounting Officer
          Robert Charles Muchmore, Jr.    (Principal Accounting Officer


     *  William E. Bradford               Chairman of the Board and Director
----------------------------------------
          William E. Bradford

     *  Anne L. Armstrong                 Director
----------------------------------------
          Anne L. Armstrong

     *  Lord Clitheroe                    Director
----------------------------------------
          Lord Clitheroe

     *  Robert L. Crandall                Director
----------------------------------------
          Robert L. Crandall

     *  Charles J. DiBona                 Director
----------------------------------------
          Charles J. DiBona

     *  W. R. Howell                      Director
----------------------------------------
          W.R. Howell

     *  Delano E. Lewis                   Director
----------------------------------------
          Delano E. Lewis

     *  C. J. Silas                       Director
----------------------------------------
          C.J. Silas

     *  Richard J. Stegemeier             Director
----------------------------------------
          Richard J. Stegemeier

     *  Lawrence S. Eagleburger           Director
----------------------------------------
          Lawrence S. Eagleburger

     *  Ray L. Hunt                       Director
----------------------------------------
          Ray L. Hunt

     *  J. Landis Martin                  Director
----------------------------------------
          J. Landis Martin

     *  Jay A. Precourt                   Director
----------------------------------------
          Jay A. Precourt

     *By:/s/Susan S. Keith
---------------------------------------- 
              Susan S. Keith
              Attorney-in-Fact

                                      -5-
<PAGE>
 
                                 EXHIBIT INDEX

 
                                                                    Sequentially
Exhibit                                                               Numbered
Number                             Description                          Page
------                             -----------                      ------------
  4.1   Restated Certificate of Incorporation of the Registrant 
        (incorporated by reference to Exhibit 3(a) to the Registrant's 
        Quarterly Report on Form 10-Q for the quarter ended June 30, 
        1998 (Exchange Act Registration No. 1-03492) filed with the 
        Commission on August 12, 1998).

  4.2   By-Laws, as amended, of the Registrant (incorporated by 
        reference to Exhibit 3.2 to the Registrant's Registration 
        Statement on Form S-3 (Registration No. 333-32731) filed with 
        the Commission on August 1, 1997).

  5.1   Opinion of Vinson & Elkins L.L.P. regarding legality.

 23.1   Consent of Arthur Andersen L.L.P.

 23.2   Consent of Vinson & Elkins L.L.P. (included in Exhibit 5.1).

 24.1   Powers of Attorney.

                                      -6-
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 20613}]
{"company-data": {"conformed-name": "HALLIBURTON CO", "cik": "0000045012", "assigned-sic": "1600", "irs-number": "752677995", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-65373", "film-number": "98721466"}, "business-address": {"street1": "3600 LINCOLN PLZ", "street2": "500 N AKARD ST", "city": "DALLAS", "state": "TX", "zip": "75201-3391", "phone": "2149782600"}, "former-company": {"former-conformed-name": "HALLIBURTON OIL WELL CEMENTING CO", "date-changed": "19660911"}}
AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON OCTOBER 6, 1998
                                                     Registration No. 333-
================================================================================

                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549

                               -----------------

                                   FORM S-8
                            REGISTRATION STATEMENT
                                     UNDER
                          THE SECURITIES ACT OF 1933

                               -----------------

                              HALLIBURTON COMPANY
            (Exact name of registrant as specified in its charter)

          DELAWARE                                         75-2677995
(State or other jurisdiction of                         (I.R.S. Employer
incorporation or organization)                         Identification No.)

                              3600 LINCOLN PLAZA
                            500 NORTH AKARD STREET
                           DALLAS, TEXAS  75201-3391
         (Address of principal executive offices, including zip code)

                               -----------------

               DRESSER INDUSTRIES, INC. 1982 STOCK OPTION PLAN*

        DRESSER INDUSTRIES, INC. 1989 RESTRICTED INCENTIVE STOCK PLAN*

            DRESSER INDUSTRIES, INC. 1992 STOCK COMPENSATION PLAN*

STOCK OPTIONS GRANTED BY DRESSER INDUSTRIES, INC. TO THE FOLLOWING FORMER NON-
                              EMPLOYEE DIRECTORS:
SAMUEL B. CASEY, JR., LAWRENCE S. EAGLEBURGER, SYLVIA A. EARLE, RAWLES FULGHAM,
JOHN A. GAVIN, RAY L. HUNT, J. LANDIS MARTIN, LIONEL H. OLMER, JAY A. PRECOURT, 
                              RICHARD W. VIESER*

              DRESSER INDUSTRIES, INC. DEFERRED COMPENSATION PLAN
                         FOR NON-EMPLOYEE DIRECTORS/+/

            DRESSER INDUSTRIES, INC. DEFERRED COMPENSATION PLAN/+/

         BAROID CORPORATION 1990 LONG TERM PERFORMANCE INCENTIVE PLAN*

     WHEATLEY TXT CORPORATION 1990 AMENDED AND RESTATED STOCK OPTION PLAN*

                           (Full title of the plans)

                               -----------------

                                                        Copy to:
              LESTER L. COLEMAN
 EXECUTIVE VICE PRESIDENT AND GENERAL COUNSEL      WILLIAM E. JOOR III
             HALLIBURTON COMPANY                 VINSON & ELKINS L.L.P.
              3600 LINCOLN PLAZA                   1001 FANNIN STREET
            500 NORTH AKARD STREET                2300 FIRST CITY TOWER
          DALLAS, TEXAS  75201-3391             HOUSTON, TEXAS 77002-6760
   (Name and address of agent for service)

                                (214) 978-2600
         (Telephone number, including area code, of agent for service)

                        CALCULATION OF REGISTRATION FEE
===================================================================================================================
 Title of securities        Amount to be           Proposed maximum          Proposed maximum         Amount of
   to be registered          registered        offering price per share  aggregate offering price  registration fee
-------------------------------------------------------------------------------------------------------------------
Common Stock,           4,023,450 shares/(2)/         $34.20/(4)/         $137,601,990/(4)/
$2.50 par value/(1)/    3,300,000 shares/(3)/         $27.84375/(5)/      $ 91,884,375/(5)/         $67,699 
===================================================================================================================
(1)  This Registration Statement also pertains to rights to purchase shares of
     Series A Junior Participating Preferred Stock of the Registrant. One right
     is attached to and trades with each share of Common Stock. Until the
     occurrence of certain events, the rights are not exercisable and will not
     be evidenced or transferred a part from the Common Stock. Any value
     attributable to such rights is reflected in the market price of the Common
     Stock.
(2)  Number of shares registered that may be issued pursuant to the Plans
     identified by an "*."
(3)  Number of shares registered that may be issued pursuant to the Plans
     identified by an "+."
(4)  Estimated, solely for purposes of calculating the registration fee, in
     accordance with Rule 457(h), based upon the weighted average exercise price
     of the options granted pursuant to the Plans described in Note 1 above.
(5)  Estimated solely for purposes of calculating the registration fee, in
     accordance with Rule 457(h), on the basis of the price of securities of the
     same class, as determined in accordance with Rule 457(c), using the average
     of the high and low prices reported on the New York Stock Exchange for the
     Common Stock on October 2, 1998. 

================================================================================
PART II
              INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.   INCORPORATION OF DOCUMENTS BY REFERENCE.

     The following documents, which have been filed with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Exchange Act
of 1934, as amended (the "Exchange Act"), by Halliburton Company (Exchange Act
Registration No. 1-03492), a Delaware corporation (the "Registrant"), are
incorporated herein by reference and made a part hereof:

          (a)  Annual Report on Form 10-K for the fiscal year ended December
               31, 1997;

          (b)  Quarterly Reports on Form 10-Q for the quarters ended March 31,
               1998 and June 30, 1998;

          (c)  Current Reports on Form 8-K filed with the Commission on January
               2, 1998; January 28, 1998; February 2, 1998; February 20, 1998;
               March 2, 1998; March 24, 1998; April 23, 1998; April 23, 1998;
               May 13, 1998; May 20, 1998; June 2, 1998; June 25, 1998; June 25,
               1998; July 9, 1998; July 16, 1998; July 16, 1998; July 21, 1998;
               July 24, 1998; July 24, 1998; August 24, 1998; September 1, 1998;
               and October 5, 1998.

          (d)  The description of the Common Stock contained in the Registration
               Statement on Form 8-B filed with the Commission on December 12,
               1996.

     All documents filed by the Registrant pursuant to Sections 13(a), 13(c), 14
and 15(d) of the Exchange Act subsequent to the effective date of this
Registration Statement, prior to the filing of a post-effective amendment to
this Registration Statement indicating that all securities offered hereby have
been sold or deregistering all securities then remaining unsold, shall be deemed
to be incorporated by reference herein and to be a part hereof from the date of
filing of such documents.  Any statement contained herein or in any document
incorporated or deemed to be incorporated by reference herein shall be deemed to
be modified or superseded for purposes of this Registration Statement to the
extent that a statement contained herein or in any other subsequently filed
document which also is or is deemed to be incorporated by reference herein
modifies or supersedes such statement.  Any such statement so modified or
superseded shall not be deemed to constitute a part of this Registration
Statement, except as so modified or superseded.

     The consolidated financial statements included in the Registrant's Annual
Reports on Form 10-K incorporated herein by reference have been audited by
Arthur Andersen LLP, independent public accountants, as indicated in their
reports with respect thereto, and are included herein in reliance upon the
authority of said firm as experts in accounting and auditing in giving said
reports.

ITEM 4.   DESCRIPTION OF SECURITIES.

     Not applicable.

ITEM 5.   INTERESTS OF NAMED EXPERTS AND COUNSEL.

     None.

ITEM 6.   INDEMNIFICATION OF DIRECTORS AND OFFICERS.

     Under Section 145 of the General Corporation Law of the State of Delaware
(the "DGCL"), a Delaware corporation has the power, under specified
circumstances, to indemnify its directors, officers, employees and agents in
connection with threatened, pending or completed actions, suits or proceedings,
whether civil, criminal, administrative or investigative (other than an action
by or in right of the corporation), brought against them by reason of the fact
that they were or are such directors, officers, employees or agents, against
expenses, judgments, fines and amounts paid in settlement actually and
reasonably incurred in any such action, suit or proceeding. Article X of the
Registrant's Restated Certificate of Incorporation together with Section 39 of
its By-Laws provide for indemnification of each person who is or was made a
party to any actual or threatened civil, criminal, administrative or
investigative action, suit or proceeding because such person is or was an
officer or director of the Registrant or is a person who is or was serving

                                      -2-
at the request of the Registrant as a director, officer, employee or agent of
another corporation or of a partnership, joint venture trust or other
enterprise, including service relating to employee benefit plans, to the fullest
extent permitted by the DGCL as it existed at the time the indemnification
provisions of the Registrant's Restated Certificate of Incorporation and By-Laws
were adopted or as may be thereafter amended. Section 39 of the Registrant's By-
Laws and Article X of its Restated Certificate of Incorporation expressly
provide that they are not the exclusive methods of indemnification.

     Section 39 of the By-Laws provides that the Registrant may maintain
insurance, at its own expense, to protect itself and any director, officer,
employee or agent of the Registrant or of any other entity against any expense,
liability or loss, regardless of whether the Registrant would have the power to
indemnify such person against such expense, liability or loss under the DGCL.

     Section 102(b)(7) of the DGCL provides that a certificate of incorporation
may contain a provision eliminating or limiting the personal liability of a
director to the corporation or its stockholders for monetary damages for breach
of fiduciary duty as a director, provided that such provision shall not
eliminate or limit the liability of a director (i) for any breach of the
director's duty of loyalty to the corporation or its stockholders, (ii) for acts
or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (iii) under Section 174 of the DGCL (relating to
liability for unauthorized acquisitions or redemptions of, or dividends on,
capital stock) or (iv) for any transaction from which the director derived an
improper personal benefit. Article XV of the Registrant's Restated Certificate
of Incorporation contains such a provision.

ITEM 7.   EXEMPTION FROM REGISTRATION CLAIMED.

     Not applicable.

ITEM 8.   EXHIBITS.

     Unless otherwise indicated below as being incorporated by reference to
another filing of the Registrant with the Commission, each of the following
exhibits is filed herewith:

      4.1 -    Restated Certificate of Incorporation of the Registrant
               (incorporated by reference to Exhibit 3(a) to the Registrant's
               Quarterly Report on Form 10-Q for the quarter ended June 30, 1998
               (Exchange Act Registration No. 1-03492) filed with the Commission
               on August 12, 1998).

      4.2 -    By-Laws, as amended, of the Registrant (incorporated by reference
               to Exhibit 3.2 to the Registrant's Registration Statement on Form
               S-3 (Registration No. 333-32731) filed with the Commission on
               August 1, 1997).

      5.1 -    Opinion of Vinson & Elkins L.L.P. regarding legality.

     23.1 -    Consent of Arthur Andersen L.L.P.

     23.2 -    Consent of Vinson & Elkins L.L.P. (included in Exhibit 5.1).

     24.1 -    Powers of Attorney.

                                 UNDERTAKINGS

     The Registrant hereby undertakes:

     (1)  To file, during any period in which offers or sales are being made, a
post-effective amendment to this Registration Statement:

          (a)  To include any prospectus required by Section 10(a)(3) of the
     Securities Act of 1933, as amended (the "Securities Act");

          (b)  To reflect in the prospectus any facts or events arising after
     the effective date of this Registration Statement (or the most recent post-
     effective amendment thereof) which, individually or in the aggregate,
     represent a fundamental change in the information set forth in this
     Registration Statement;

                                      -3-
(c)  To include any material information with respect to the plan of
     distribution not previously disclosed in this Registration Statement or any
     material change to such information in this Registration Statement;

provided, however, that paragraphs (1)(a) and (1)(b) do not apply if the
information required to be included in a post-effective amendment by those
paragraphs is contained in periodic reports filed by the Registrant pursuant to
Section 13 or Section 15(d) of the Exchange Act that are incorporated by
reference in this Registration Statement.

     (2)  That, for the purpose of determining any liability under the
Securities Act, each such post-effective amendment shall be deemed to be a new
registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.

     (3)  To remove from registration by means of a post-effective amendment any
of the securities being registered which remain unsold at the termination of the
offering.

     (4)  That, for the purposes of determining any liability under the
Securities Act, each filing of the Registrant's annual report pursuant to
Section 13(a) or Section 15(d) of the Exchange Act (and, where applicable, each
filing of an employee benefit plan's annual report pursuant to Section 15(d) of
the Exchange Act) that is incorporated by reference in this Registration
Statement shall be deemed to be a new registration statement relating to the
securities offered therein, and the offering of such securities at that time
shall be deemed to be the initial bona fide offering thereof.

     (5)  Insofar as indemnification for liabilities arising under the
Securities Act may be permitted to directors, officers and controlling persons
of the Registrant pursuant to the foregoing provisions, or otherwise, the
Registrant has been advised that in the opinion of the Commission such
indemnification is against public policy as expressed in the Securities Act and
is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the Registrant of expenses
incurred or paid by a director, officer or controlling person of the Registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the Registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.

                                      -4-
SIGNATURES

Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Dallas, State of Texas, on the 5th day of October,
1998.

                                      HALLIBURTON COMPANY

                                      By:  /s/ Richard B. Cheney
                                           -------------------------------------
                                           Richard B. Cheney
                                           Chief Executive Officer

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated on the 5th day of October, 1998.

               Signature                                Title
               ---------                                -----

     /s/  Richard B. Cheney               Chief Executive Officer and Director
----------------------------------------  (Principal Executive Officer)
          Richard B. Cheney

     /s/  Gary V. Morris                  Executive Vice President and Chief 
----------------------------------------  Financial Officer (Principal Financial
          Gary V. Morris                  Officer

     /s/  Robert Charles Muchmore, Jr.    Vice President, Controller and 
----------------------------------------  Principal Accounting Officer
          Robert Charles Muchmore, Jr.    (Principal Accounting Officer

     *  William E. Bradford               Chairman of the Board and Director
----------------------------------------
          William E. Bradford

     *  Anne L. Armstrong                 Director
----------------------------------------
          Anne L. Armstrong

     *  Lord Clitheroe                    Director
----------------------------------------
          Lord Clitheroe

     *  Robert L. Crandall                Director
----------------------------------------
          Robert L. Crandall

     *  Charles J. DiBona                 Director
----------------------------------------
          Charles J. DiBona

     *  W. R. Howell                      Director
----------------------------------------
          W.R. Howell

     *  Delano E. Lewis                   Director
----------------------------------------
          Delano E. Lewis

     *  C. J. Silas                       Director
----------------------------------------
          C.J. Silas

     *  Richard J. Stegemeier             Director
----------------------------------------
          Richard J. Stegemeier

     *  Lawrence S. Eagleburger           Director
----------------------------------------
          Lawrence S. Eagleburger

     *  Ray L. Hunt                       Director
----------------------------------------
          Ray L. Hunt

     *  J. Landis Martin                  Director
----------------------------------------
          J. Landis Martin

     *  Jay A. Precourt                   Director
----------------------------------------
          Jay A. Precourt

     *By:/s/Susan S. Keith
---------------------------------------- 
              Susan S. Keith
              Attorney-in-Fact

                                      -5-
EXHIBIT INDEX

 
                                                                    Sequentially
Exhibit                                                               Numbered
Number                             Description                          Page
------                             -----------                      ------------
  4.1   Restated Certificate of Incorporation of the Registrant 
        (incorporated by reference to Exhibit 3(a) to the Registrant's 
        Quarterly Report on Form 10-Q for the quarter ended June 30, 
        1998 (Exchange Act Registration No. 1-03492) filed with the 
        Commission on August 12, 1998).

  4.2   By-Laws, as amended, of the Registrant (incorporated by 
        reference to Exhibit 3.2 to the Registrant's Registration 
        Statement on Form S-3 (Registration No. 333-32731) filed with 
        the Commission on August 1, 1997).

  5.1   Opinion of Vinson & Elkins L.L.P. regarding legality.

 23.1   Consent of Arthur Andersen L.L.P.

 23.2   Consent of Vinson & Elkins L.L.P. (included in Exhibit 5.1).

 24.1   Powers of Attorney.

                                      -6-