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                                                                    EXHIBIT 1.1



                             SOUTHWEST AIRLINES CO.
                                DEBT SECURITIES
                                TERMS AGREEMENT

                               February 25, 1997

To:      Southwest Airlines Co.
         2702 Love Field Drive
         Dallas, Texas  75235

Dear Sirs:

         We understand that Southwest Airlines Co., a Texas corporation (the
"Company"), proposes to issue and sell $100,000,000 aggregate principal amount
of debt securities. On behalf of the Underwriters named in Schedule I hereto
(the "Underwriters"), and subject to the terms and conditions set forth herein
or incorporated by reference herein, we hereby offer to purchase such
Securities.

         The Securities to be purchased by the Underwriters, which are to be 
issued under an Indenture dated as of February 25, 1997 between the Company and
U.S. Trust Company of Texas, N.A., as Trustee, shall have the following terms:


                                                           
         Title:                                               73/8% Debentures Due 2027

         Principal amount to be issued:                       $100,000,000

         Date of maturity:                                    March 1, 2027

         Interest rate:                                       73/8% per annum

         Interest payment dates:                              March 1 and September 1 of each year,
                                                              beginning September 1, 1997, in immediately
                                                              available funds

         Public offering price:                               99.639%, plus accrued interest from Feb-
                                                              ruary 28, 1997

         Purchase price:                                      98.764%, plus accrued interest from
                                                              February 28, 1997 (payable in same-day
                                                              funds)

         Redemption provisions:                               Redeemable, at the option of the Company, in
                                                              whole at any time or in part from time to time,
                                                              at a redemption price equal to the greater of
                                                              (i) 100% of their principal amount and (ii) the
                                                              sum of the present values of the remaining
                                                              scheduled payments of principal and interest



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                                                              thereon discounted to the date of redemption,
                                                              on a semiannual basis (assuming a 360-day year
                                                              consisting of twelve 30-day months), at the
                                                              Treasury Rate (as defined) plus 20 basis
                                                              points, plus accrued interest thereon to the
                                                              date of redemption.

         Defeasance:                                          Yes

         Delayed Delivery Contracts:                          None

         Book-entry arrangements:                             Authorized

         Underwriters' counsel:                               Vinson & Elkins L.L.P., Houston, Texas

         Closing date and location:                           February 28, 1997, at the offices of the
                                                              Company, 2702 Love Field Drive, Dallas,
                                                              Texas

         Current ratings:                                     Moody's Investor Service -- A3
                                                              Standard & Poor's -- A-
                                                              Duff & Phelps -- A-


         All of the provisions contained in the document entitled "Southwest
Airlines Co. Debt Securities, Underwriting Agreement--Basic Provisions," dated
as of September 1, 1992, a copy of which is attached hereto as Annex A, are
herein incorporated by reference in their entirety, except to the extent
inconsistent herewith, and shall be deemed to be a part of this Terms Agreement
to the same extent as if such provisions had been set forth in full herein.
Terms defined in such document are used herein as therein defined, except that
the references therein to the Indenture dated as of June 21, 1991 shall be
deemed to be the Indenture as defined in this Terms Agreement and the
registration statement on Form S-3 (No. 33-50930) referred to therein shall be
deemed to be the Company's registration statement on Form S-3 (No. 33-59113).
The Underwriters severally agree, subject to the terms and provisions of this
Terms Agreement, including the terms and provisions incorporated by reference
herein, to purchase from the Company the respective principal amounts of
Securities set forth opposite their names in Schedule I hereto.

         The Company and the Underwriters acknowledge that Vinson & Elkins
L.L.P., which is acting as counsel to the Underwriters in connection with the
offer and sale of the Securities, also acts as counsel from time to time to the
Company in connection with unrelated matters. The Company and the Underwriters
consent to such firm's so acting as counsel to the Underwriters and as counsel
to the Company.



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         Any notice by the Company to the Underwriters pursuant to this Terms
Agreement shall be in writing and shall be deemed to have been duly given if
mailed or transmitted by any standard form of telecommunication addressed to
the Underwriters c/o Lehman Brothers Inc., 3 World Financial Center, 200 Vesey
Street, New York, New York 10285.

         Please accept this offer by signing a copy of this Terms Agreement in
the space set forth below and returning the signed copy to us.

                                  LEHMAN BROTHERS INC.
                                  MERRILL LYNCH & CO.
                                       Merrill Lynch, Pierce, Fenner & Smith
                                            Incorporated
                                  SALOMON BROTHERS INC

                                  By:   Lehman Brothers Inc.

                                  By:  /s/ Peter Wexler
                                     -------------------------------------------
                                  Title:  Managing Director
                                        ----------------------------------------



Accepted:

SOUTHWEST AIRLINES CO.


By:  /s/ Gary C. Kelly
   ---------------------------
Title:  Vice President & CEO
   ---------------------------





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                                   SCHEDULE I







                                                                                                PRINCIPAL
                                  UNDERWRITER                                                    AMOUNT
                                  -----------                                                    ------
                                                                                          
Lehman Brothers Inc.....................................................................     $  33,400,000

Merrill Lynch, Pierce, Fenner & Smith Incorporated......................................        33,300,000

Salomon Brothers Inc....................................................................        33,300,000
                                                                                              ------------
         Total...........................................................................     $100,000,000
                                                                                              ============






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