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              As filed with the Securities and Exchange Commission
                              on November 20, 1998

                                                              Reg. No. 333-_____

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM S-8
                             Registration Statement
                                      Under
                           The Securities Act of 1933

                             SOUTHWEST AIRLINES CO.
             (Exact name of registrant as specified in its charter)

         Texas                                          75-1563240
(State or other jurisdiction of                      (I.R.S. Employer
incorporation or organization)                      Identification No.)

P.O. Box 36611, Dallas, Texas                             75235-1611
(Address of Principal Executive Offices)                  (Zip Code)

                             Southwest Airlines Co.
                   Southwest Airlines Co. Excess Benefit Plan
                            (Full title of the plan)

                                  Gary C. Kelly
                Vice President-Finance & Chief Financial Officer
                             Southwest Airlines Co.
                                 P.O. Box 36611
                            Dallas, Texas 75235-1611
                                  214/792-4363
           (Name, address, and telephone number, including area code,
                              of agent for service)

                                    Copy to:

                                Deborah Ackerman
                            Associate General Counsel
                             Southwest Airlines Co.
                                 P.O. Box 36611
                            Dallas, Texas 75235-1611

                         CALCULATION OF REGISTRATION FEE
- --------------------------------------------------------------------------------
                                                  Proposed
                                 Proposed         maximum          Amount
Title of                         maximum          aggregate        of
securities to     Amount to be   offering price   offering         registra-
be registered     registered     per share(2)     price(2)         tion fee
- --------------------------------------------------------------------------------
Deferred
Compensation
Obligations(1)    $6,000,000        100%         $6,000,000        $1,668

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

     (1) The Deferred Compensation Obligations are unsecured obligations of
     Southwest Airlines Co. to pay deferred compensation in the future in
     accordance with the terms of the Southwest Airlines Co. Excess Benefit Plan
     for a select group of eligible employees.

     (2) The amount to be registered is estimated solely for purposes of
     calculating the registration fee.



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                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT


Item 3.  Incorporation of Documents by Reference.

         The following documents filed with the Securities and Exchange
Commission (the "Commission") are incorporated herein by reference:

         (a)   the Company's latest annual report filed pursuant to Section 13
or 15(d) of the Securities Exchange Act of 1934;

         (b)   all other reports filed pursuant to Section 13(a) or 15(d) of the
Securities Exchange Act of 1934 since the end of the fiscal year covered by the
annual report referred to above; and

         All reports and other documents subsequently filed by the Company
pursuant to Section 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of
1934, as amended, prior to the filing of a post-effective amendment which
indicates that all securities offered hereby have been sold or which deregisters
all securities remaining unsold, shall be deemed to be incorporated by reference
herein and to be a part hereof from the date of filing of such reports and
documents.

Item 4.  Description of Securities.

         The Deferred Compensation Obligations registered hereunder (the
"Obligations") are unsecured obligations of the Registrant to pay deferred
compensation in the future in accordance with the terms of the Southwest
Airlines Co. Excess Benefit Plan (the "Plan"). Southwest Airlines Co. will
appoint an independent trustee which must be a national bank with capital and
surplus not less than $100 million. The Plan is filed as Exhibit 4.1 to this
Registration Statement. Such Exhibit sets forth a description of the Obligations
and is incorporated herein by reference in its entirety in response to this Item
4, pursuant to Rule 411(b)(3) under the Securities Act of 1933.

         No participant under the Plan shall have any preferred claim to, or any
beneficial ownership interest in, any assets from which the Obligations will be
paid. All such assets are subject to the claims of the creditors of Southwest
Airlines Co. until they are paid to the participant in accordance with the terms
of the Plan.


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Item 6.  Indemnification of Directors and Officers.

         Article VIII, Section 1 of Registrant's Bylaws provides as follows:

         "Right to Indemnification: Subject to the limitations and conditions as
provided in this Article VIII, each person, who was or is made a party to, or is
threatened to be made a party to, any threatened, pending or completed action,
suit or proceeding, whether civil, criminal, administrative, arbitrative or
investigative (hereinafter called a "proceeding"), or any appeal in such a
proceeding or any inquiry or investigation that could lead to such a proceeding,
by reason of the fact that he (or a person of whom he is the legal
representative) is or was a director or officer of the corporation (or while a
director or officer of the corporation is or was serving at the request of the
corporation as a director, officer, partner, venturer, proprietor, trustee,
employee, agent, or similar functionary of another foreign or domestic
corporation, partnership, joint venture, proprietorship, trust, employee benefit
plan, or other enterprise) shall be indemnified by the corporation to the
fullest extent permitted by the Texas Business Corporation Act, as the same
exists or may hereafter be amended (but, in the case of any such amendment, only
to the extent that such amendment permits the corporation to provide broader
indemnification rights than said law permitted the corporation to provide prior
to such amendment) against judgments, penalties (including excise and similar
taxes and punitive damages), fines, settlements and reasonable expenses
(including, without limitation, court costs and attorneys' fees) actually
incurred by such person in connection with such proceeding, appeal, inquiry or
investigation, and indemnification under this Article VIII shall continue as to
a person who has ceased to serve in the capacity which initially entitled such
person to indemnity hereunder; provided, however, that in no case shall the
corporation indemnify any such person (or the legal representative of any such
person) otherwise than for his reasonable expenses, in respect of any proceeding
(i) in which such person shall have been finally adjudged by a court of
competent jurisdiction (after exhaustion of all appeals therefrom) to be liable
on the basis that personal benefit was improperly received by him, whether or
not the benefit resulted from an action taken in such person's official
capacity, or (ii) in which such person shall have been found liable to the
corporation; and provided, further, that the corporation shall not indemnify any
such person for his reasonable expenses actually incurred in connection with any
proceeding in which he shall have been found liable for willful or intentional
misconduct in the performance of his duty to the corporation. The rights granted
pursuant to this Article VIII shall be deemed contract rights, and no amendment,
modification or repeal of this Article VIII shall have the effect of limiting or
denying any such rights with respect to actions taken or proceedings arising
prior to any such amendment, modification or repeal. It is expressly
acknowledged that the indemnification provided in this Article VIII could
involve indemnification for negligence or under theories of strict liability."

         Article Ten of the Company's Articles of Incorporation provides that a
director of the corporation shall not be liable to the corporation or its
shareholders for monetary damages for an act or omission in the director's
capacity as a director, subject to certain limitations.

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         Article 2.02-1 B. of the Texas Business Corporation Act provides that,
subject to certain limitations, "a corporation may indemnify a person who was,
is or is threatened to be made a named defendant or respondent in a proceeding
because the person is or was a director only if it is determined in accordance
with Section F of this article that the person: (1) conducted himself in good
faith; (2) reasonably believed: (a) in the case of conduct in his official
capacity as a director of the corporation, that his conduct was in the
corporation's best interests; and (b) in all other cases, that his conduct was
at least not opposed to the corporation's best interests; and (3) in the case of
any criminal proceeding, had no reasonable cause to believe his conduct was
unlawful."

         The Company also maintains directors' and officers' liability
insurance.

Item 8.  Exhibits.


         4.1      Southwest Airlines Co. Excess Benefit Plan.

         5        Opinion of Deborah Ackerman, Associate General Counsel of
                  Southwest, re legality of securities being registered.

         23.1     Consent of Ernst & Young LLP, independent auditors.

         23.2     Consent of Deborah Ackerman, Associate General Counsel of
                  Southwest (contained in the opinion filed as Exhibit 5
                  hereto).

Item 9.  Undertakings.

A.       The undersigned 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 to include any
material information with respect to the plan of distribution not previously
disclosed in the registration statement or any material change to such
information in the registration statement.

         (2)   That, for the purpose of determining any liability under the
Securities Act of 1933, 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 by registration by means of a post-effective amendment
any of the securities being registered which remain unsold at the termination of
the offering.

B.       The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of

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1933, each filing of the registrant's annual report pursuant to Section 13(a) or
Section 15(d) of the Securities Exchange Act of 1934 that is incorporated by
reference in the 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.

C.       Insofar as indemnification for liabilities arising under the Securities
Act of 1933 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 Securities and Exchange
Commission such indemnification is against public policy as expressed in the 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 Act and will be governed by the final adjudication of
such issue.

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                                   SIGNATURES

         The Registrant. Pursuant to the requirements of the Securi ties 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 November 19, 1998.

                                                    SOUTHWEST AIRLINES CO.

                                                    By   /s/ Gary C. Kelly
                                                       -------------------------
                                                         Gary C. Kelly
                                                         Vice President-Finance,
                                                         Chief Financial Officer

         Pursuant to the requirements of the Securities Exchange Act of 1933,
this Registration Statement has been signed by the following persons in the
capacities indicated on November 19, 1998.

      Signature                                            Capacity

/s/ Herbert D. Kelleher                     Chairman of the Board of Directors,
- -----------------------------------         President and Chief Executive 
Herbert D. Kelleher                         Officer

/s/ Gary C. Kelly                           Vice President-Finance
- -----------------------------------         (Chief Financial and Accounting
Gary C. Kelly                               Officer)

/s/ Samuel E. Barshop                       Director
- -----------------------------------
Samuel E. Barshop

/s/ Gene H. Bishop                          Director
- -----------------------------------
Gene H. Bishop

/s/ William P. Hobby                        Director
- -----------------------------------
William P. Hobby

/s/ Travis C. Johnson                       Director
- -----------------------------------
Travis C. Johnson

/s/ R. W. King                              Director
- -----------------------------------
R. W. King

/s/Walter M. Mischer, Sr.Director
- -----------------------------------
Walter M. Mischer, Sr.

/s/ June M. Morris                          Director
- -----------------------------------
June M. Morris

/s/ C. Webb Crockett                        Director
- -----------------------------------
C. Webb Crockett

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                                INDEX TO EXHIBITS





       EXHIBIT 
       NUMBER                 DESCRIPTION
       -------                -----------

               
         4.1      Southwest Airlines Co. Excess Benefit Plan.

         5        Opinion of Deborah Ackerman, Associate General Counsel of
                  Southwest, re legality of securities being registered.

         23.1     Consent of Ernst & Young LLP, independent auditors.

         23.2     Consent of Deborah Ackerman, Associate General Counsel of
                  Southwest (contained in the opinion filed as Exhibit 5
                  hereto).