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                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

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                                    FORM 8-K

                                 CURRENT REPORT

                       Pursuant to Section 13 or 15(d) of
                       the Securities Exchange Act of 1934


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         Date of Report (Date of earliest event reported): May 21, 1998

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

            TEXAS                    1-7259                  74-1563240
(State or other jurisdiction       (Commission            (I.R.S. employee
      of incorporation)            file number)           identification no.)


                                 P.O. Box 36611
                         Love Field, Dallas, Texas 75235
               (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES) (ZIP CODE)

        Registrant's telephone number, include area code: (214) 792-4000


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Item 7.  Financial Statements and Exhibits.

         The following documents are being filed in connection with, and
incorporated by reference into, Southwest Airlines Co.'s Registration Statement
on Form S-3 (File No. 333-29257), as declared effective on July 15, 1997,
relating to Pass Through Certificates, Series 1998-A.




Exhibits
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Exhibit 1.3                -        Form of Underwriting Agreement relating to the issuance of Pass
                                    Through Certificates, Series 1998-A.

Exhibit 4.3                -        Form of Pass Through Trust Supplement No. 1998-A between
                                    Southwest and the Trustee relating to the Pass Through Certificates.


Exhibit 4.4 *              -        Form of Trust Agreement between the Owner Participant and the
                                    Owner Trustee relating to the Equipment Notes with respect to
                                    Boeing 737-3H4 Aircraft, Registration Nos. N620SW, N621SW,
                                    N622SW and N623SW.

Exhibit 4.5 *              -        Form of Trust Indenture and Security Agreement between the
                                    Owner Trustee and the Loan Trustee relating to the Equipment
                                    Notes with respect to Boeing 737-3H4 Aircraft, Registration
                                    Nos. N620SW, N621SW, N622SW and N623SW.

Exhibit 4.6 *              -        Form of First Amendment to Trust Indenture and Security
                                    Agreement between the Owner Trustee and the Loan Trustee
                                    relating to the Equipment Notes with respect to Boeing 737-3H4
                                    Aircraft, Registration Nos. N620SW, N621SW, N622SW and
                                    N623SW.

Exhibit 4.7 *              -        Form of Equipment Notes with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW
                                    (included as Exhibit A-1 in Exhibit 4.6).

Exhibit 4.8 *              -        Form of Participation Agreement among Southwest, the Owner
                                    Participant, the Loan Trustee, the Original Loan Participant, and the
                                    Owner Trustee with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW.

Exhibit 4.9 *              -        Form of First Amendment to Participation Agreement among
                                    Southwest, the Owner Participant, the Owner Trustee, the Loan
                                    Trustee and the Trustee with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW.



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Exhibit 4.10 *             -        Form of Sale and Lease Agreement between Southwest and the
                                    Owner Trustee with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW.

Exhibit 4.11 *             -        Form of First Amendment to Sale and Lease Agreement between
                                    Southwest and the Owner Trustee with respect to Boeing 737-3H4
                                    Aircraft, Registration Nos. N620SW, N621SW, N622SW and
                                    N623SW.

Exhibit 4.12 *             -        Form of Refinancing Agreement among Southwest, the Trustee, the
                                    Owner Participant, the Owner Trustee, the Loan Trustee and the
                                    Original Loan Participant relating to the Equipment Notes for each
                                    of four Boeing 737-3H4 Aircraft, Registration Nos. N620SW,
                                    N621SW, N622SW and N623SW.

Exhibit 23                 -        Consent of Independent Auditors



         *The financing of each of the identified aircraft pursuant to Pass
Through Certificates is documented separately. Pursuant to Instruction 2 to Item
601 of Regulation S-K, the Registrant has filed the form of the indicated
documents for one of these aircraft only -- specifically, the aircraft with
Registration No. N620SW (or, in the case of Exhibit 4.10, with Registration No.
N621SW). The documents for the other aircraft are identical except for the
information identifying the aircraft in question, the name of the trust
established to own such aircraft, and information relating to the identity of
the Owner Participant, which is C.C.& E.II, LLC with respect to the aircraft
with Registration No. N622SW and Chrysler Asset Management Corporation with
respect to the aircraft with Registration No. N623SW.


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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 thereunto duly authorized.

                                    SOUTHWEST AIRLINES CO.



May 28, 1998                        By: /s/ Gary C. Kelly
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                                            Gary C. Kelly
                                            Vice President -- Finance
                                            and Chief Financial Officer


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                                  EXHIBIT INDEX




Exhibit No.                                          Description
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Exhibit 1.3                -        Form of Underwriting Agreement relating to the issuance of Pass
                                    Through Certificates, Series 1998-A.

Exhibit 4.3                -        Form of Pass Through Trust Supplements No. 1998-A between
                                    Southwest and the Trustee relating to the Pass Through Certificates.

Exhibit 4.4 *              -        Form of Trust Agreement between the Owner Participant and the
                                    Owner Trustee relating to the Equipment Notes with respect to
                                    Boeing 737-3H4 Aircraft, Registration Nos. N620SW, N621SW,
                                    N622SW and N623SW.

Exhibit 4.5 *              -        Form of Trust Indenture and Security Agreement between the
                                    Owner Trustee and the Loan Trustee relating to the Equipment
                                    Notes with respect to Boeing 737-3H4 Aircraft, Registration Nos.
                                    N620SW, N621SW, N622SW and N623SW.

Exhibit 4.6 *              -        Form of First Amendment to Trust Indenture and Security
                                    Agreement between the Owner Trustee and the
                                    Loan Trustee relating to the Equipment Notes
                                    with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and
                                    N623SW.

Exhibit 4.7 *              -        Form of Equipment Notes with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW
                                    (included as Exhibit A-1 in Exhibit 4.6).

Exhibit 4.8 *              -        Form of Participation Agreement among Southwest, the Owner
                                    Participant, the Loan Trustee, the Original Loan Participant, and the
                                    Owner Trustee with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW.

Exhibit 4.9 *              -        Form of First Amendment to Participation Agreement among
                                    Southwest, the Owner Participant, the Owner Trustee, the Loan
                                    Trustee and the Trustee with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW.

Exhibit 4.10 *             -        Form of Sale and Lease Agreement between Southwest and the
                                    Owner Trustee with respect to Boeing 737-3H4 Aircraft,
                                    Registration Nos. N620SW, N621SW, N622SW and N623SW.



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Exhibit No.                                          Description
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Exhibit 4.11 *             -        Form of First Amendment to Sale and Lease Agreement between
                                    Southwest and the Owner Trustee with respect to Boeing 737-3H4
                                    Aircraft, Registration Nos. N620SW, N621SW, N622SW and
                                    N623SW.

Exhibit 4.12 *             -        Form of Refinancing Agreement among Southwest, the Trustee, the
                                    Owner Participant, the Owner Trustee, the Loan Trustee and the
                                    Original Loan Participant relating to the Equipment Notes for each
                                    of four Boeing 737-3H4 Aircraft, Registration Nos. N620SW,
                                    N621SW, N622SW and N623SW.

Exhibit 23                 -        Consent of Independent Auditors




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