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                                                                    EXHIBIT 25.1

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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                    FORM T-1

STATEMENT OF ELIGIBILITY UNDER THE TRUST INDENTURE ACT OF 1939 OF A CORPORATION
                         DESIGNATED TO ACT AS TRUSTEE

             CHECK IF AN APPLICATION TO DETERMINE ELIGIBILITY OF A
                 TRUSTEE PURSUANT TO SECTION 305(b)(2)   X
                                                       ------

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

                       U.S. TRUST COMPANY OF TEXAS, N.A.
              (Exact name of trustee as specified in its charter)



                                                        75-2353745
      (State of incorporation                        (I.R.S. employer
      if not a national bank)                      identification No.)

                                                   
    2001 Ross Avenue, Suite 2700                        75201-2936
           Dallas, Texas                                (Zip Code)
       (Address of trustee's                       
    principal executive offices)
    

                               Compliance Officer
                       U.S. Trust Company of Texas, N.A.
                          2001 Ross Avenue, Suite 2700
                           Dallas, Texas  75201-2936
                                 (214) 754-1200
           (Name, address and telephone number of agent for service)

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

                             Southwest Airlines Co.
              (Exact name of obligor as specified in its charter)



                       Texas                                 74-1563240
          (State or other jurisdiction of                 (I.R.S. employer
           incorporation or organization)               identification No.)
                                                        
               2702 Love Field Drive                    
                    Dallas, TX                                 75235
      (Address of principal executive offices)               (Zip Code)
                                                     
                            --------------------

                               Debt Securities
                     (Title of the indenture securities)


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                                    GENERAL

1.       General Information.

         Furnish the following information as to the Trustee:

         (a)     Name and address of each examining or supervising authority to
                 which it is subject.

                          Federal Reserve Bank of Dallas (11th District),
                          Dallas, Texas (Board of Governors of the Federal
                          Reserve System)
                          Federal Deposit Insurance Corporation, Dallas, Texas
                          The Office of the Comptroller of the Currency,
                          Dallas, Texas

         (b)     Whether it is authorized to exercise corporate trust powers.

                          The Trustee is authorized to exercise corporate trust
                          powers.

2.       Affiliations with Obligor and Underwriters.

         If the obligor or any underwriter for the obligor is an affiliate of
         the Trustee, describe each such affiliation.

         None.

3.       Voting Securities of the Trustee.

         Furnish the following information as to each class of voting
         securities of the Trustee:

                            As of January 31, 1997


- --------------------------------------------------------------------------------
         Col A.                                                 Col B.
- --------------------------------------------------------------------------------
                                                     
    Title of Class                                       Amount Outstanding
- --------------------------------------------------------------------------------
Capital Stock - par value $100 per share                     5,000 shares
- --------------------------------------------------------------------------------


4.       Trusteeships under Other Indentures.

         Not Applicable

5.       Interlocking Directorates and Similar Relationships with the Obligor
         or Underwriters.

         Not Applicable
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6.       Voting Securities of the Trustee Owned by the Obligor or its
         Officials.

         Not Applicable

7.       Voting Securities of the Trustee Owned by Underwriters or their
         Officials.

         Not Applicable

8.       Securities of the Obligor Owned or Held by the Trustee.

         Not Applicable

9.       Securities of Underwriters Owned or Held by the Trustee.

         Not Applicable

10.      Ownership or Holdings by the Trustee of Voting Securities of Certain
         Affiliates or Security Holders of the Obligor.

         Not Applicable

11.      Ownership or Holdings by the Trustee of any Securities of a Person
         Owning 50 Percent or More of the Voting Securities of the Obligor.

         Not Applicable

12.      Indebtedness of the Obligor to the Trustee.

         Not Applicable

13.      Defaults by the Obligor.

         Not Applicable

14.      Affiliations with the Underwriters.

         Not Applicable

15.      Foreign Trustee.

         Not Applicable

16.      List of Exhibits.

         T-1.1   -  A copy of the Articles of Association of U.S. Trust Company
                    of Texas, N.A.; incorporated herein by reference to Exhibit
                    T-1.1 filed with Form T-1 Statement, Registration No.
                    22-21897.
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16.      (con't.)

         T-1.2   -  A copy of the certificate of authority of the Trustee to
                    commence business; incorporated herein by reference to
                    Exhibit T-1.2 filed with Form T-1 Statement, Registration
                    No. 22-21897.

         T-1.3   -  A copy of the authorization of the Trustee to exercise
                    corporate trust powers; incorporated herein by reference to
                    Exhibit T-1.3 filed with Form T-1 Statement, Registration
                    No. 22-21897.

         T-1.4   -  A copy of the By-laws of the U.S. Trust Company of Texas,
                    N.A., as amended to date; incorporated herein by reference
                    to Exhibit T-1.4 filed with Form T-1 Statement,
                    Registration No. 22-21897.

         T-1.5   -  The consent of the Trustee required by Section 321(b) of
                    the Trust Indenture Act of 1939.

         T-1.6   -  A copy of the latest report of condition of the Trustee
                    published pursuant to law or the requirements of its
                    supervising or examining authority.


         NOTE

As of January 31, 1997 the Trustee had 5,000 shares of Capital Stock
outstanding, all of which are owned by U.S. T.L.P.O. Corp.  As of January 31,
1997 U.S. T.L.P.O. Corp. had 35 shares of Capital Stock outstanding, all of
which are owned by U.S. Trust Corporation.  U.S. Trust Corporation had
outstanding 9,863,036 shares of $5 par value Common Stock as of January 31,
1997.

The term "Trustee" in Items 2, 5, 6, 7, 8, 9, 10 and 11 refers to each of U.S
Trust Company of Texas, N.A., U.S. T.L.P.O. Corp. and U.S. Trust Corporation.

Inasmuch as this Form T-1 is filed prior to the ascertainment by the Trustee of
all the facts on which to base responsive answers to Items 2, 5, 6, 7, 9, 10
and 11, the answers to said Items are based upon incomplete information.  Items
2, 5, 6, 7, 9, 10 and 11 may, however, be considered correct unless amended by
an amendment to this Form T-1.

In answering any items in this Statement of Eligibility and Qualification which
relates to matters peculiarly within the knowledge of the obligors or their
directors or officers, or an underwriter for the obligors, the Trustee has
relied upon information furnished to it by the obligors and will rely on
information to be furnished by the obligors or such underwriter, and the
Trustee disclaims responsibility for the accuracy or completeness of such
information.


                             --------------------
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                                   SIGNATURE

Pursuant to the requirements of the Trust Indenture Act of 1939 the Trustee,
U.S Trust Company of Texas, N.A., a national banking association organized
under the laws of the United States of America, has duly caused this statement
of eligibility and qualification to be signed on its behalf by the undersigned,
thereunto duly authorized, all in the City of Dallas, and State of Texas on the
20th day of February, 1997.



                                              U.S. Trust Company of Texas, N.A.,
                                              Trustee
                                               
                                               
                                               
                                              By: /s/  JOHN C. STOHLMANN
                                                 -------------------------------
                                                     John C. Stohlmann
                                                     Vice President
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                                                                   Exhibit T-1.5



                               CONSENT OF TRUSTEE

Pursuant to the requirements of Section 321(b) of the Trust Indenture Act of
1939 as amended in connection with the proposed issue of Southwest Airlines Co.
Debt Securities, we hereby consent that reports of examination by Federal,
State, Territorial or District authorities may be furnished by such authorities
to the Securities and Exchange Commission upon request therefor.




                                         U.S. Trust Company of Texas, N.A.
                                         
                                         
                                         
                                         By:   /s/ JOHN C. STOHLMANN
                                               ------------------------------
                                                 John C. Stohlmann
                                                 Vice President
                                         
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                                                                         Board of Governors of the Federal Reserve System
                                                                         OMB Number: 7100-0036
                                                                         Federal Deposit Insurance Corporation
                                                                         OMB Number: 3064-0052
                                                                         Office of the Comptroller of the Currency
                                                                         OMB Number: 1557-0081
Federal Financial Institutions Examination Council                       Expires March 31, 1999
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                                                                                                                      [1]
[LOGO]                                                                   Please Refer to Page i,
                                                                         Table of Contents, for
                                                                         the required disclosure
                                                                         of estimated burden
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CONSOLIDATED REPORTS OF CONDITION AND INCOME FOR
A BANK WITH DOMESTIC OFFICES ONLY AND
TOTAL ASSETS OF LESS THAN $100 MILLION - FFIEC 034 

REPORT AT THE CLOSE OF BUSINESS DECEMBER 31, 1996                       (961231)
                                                                       ----------- 
                                                                       (RCRI 9999)

This report is required by law: 12 U.S.C. Section 324 (State    This report form is to be filed by banks with
member banks); 12 U.S.C. Section 1817 (State nonmember          domestic offices only. Banks with branches and
banks); and 12 U.S.C. Section 161 (National banks).             consolidated subsidiaries in U.S. territories and
                                                                possessions, Edge or Agreement subsidiaries, foreign
                                                                branches, consolidated foreign subsidiaries, or
                                                                International Banking Facilities must file FFIEC 031.
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NOTE: The Reports of Condition and Income must be signed by     The Reports of Condition and Income are to be
an authorized officer and the Report of Condition must be       prepared in accordance with Federal Regulatory
attested to by not less than two directors (trustees) for       authority instructions. NOTE: These instructions may
State nonmember banks and three directors for State member      in some cases differ from generally accepted
and National banks.                                             accounting principles.

I, Alfred B. Childs, SVP & Cashier                              We, the undersigned directors (trustees), attest to
   --------------------------------------------------------     the correctness of this Report of Condition             
   Name and Title of Officer Authorized to Sign Report          (including the supporting schedules) and declare that   
                                                                it has been examined by us and to the best of our       
of the named bank do hereby declare that these Reports of       knowledge and belief has been prepared in conformance   
Condition and Income (including the supporting schedules)       with the instructions issued by the appropriate         
have been prepared in conformance with the instructions         Federal regulatory authority and is true and correct.   
issued by the appropriate Federal regulatory authority and                                                              
are true to the best of my knowledge and belief.                /s/ STUART M. PEARMAN
                                                                -----------------------------------------------------
                                                                Director (Trustee)                
/s/ ALFRED B. CHILDS                                            
- -------------------------------------------------------------   /s/ J. T. MOORE, JR.
Signature of Officer Authorized to Sign Report                  -----------------------------------------------------
                                                                Director (Trustee)                   
                                                                
  January 15, 1997                                              /s/ PETER J. DENKER
- -------------------------------------------------------------   -----------------------------------------------------
Date of Signature                                               Director (Trustee)                   
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FOR BANKS SUBMITTING HARD COPY REPORT FORMS:

STATE MEMBER BANKS: Return the original and one copy to the     NATIONAL BANKS: Return the original only in the
appropriate Federal Reserve District Bank.                      special return address envelope provided. If express
                                                                mail is used in lieu of the special return address
STATE NONMEMBER BANKS: Return the original only in the          envelope, return the original only to the FDIC, c/o
special return address envelope provided. If express mail is    Quality Data Systems, 2127 Espey Court, Suite 204,
used in lieu of the special return address envelope, return     Crofton, MD 21114.
the original only to the FDIC, c/o Quality Data Systems,
2127 Espey Court, Suite 204, Crofton, MD 21114.
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FDIC Certificate Number                                                                                      12-31-96
                      -----------                               Banks should affix the address label in this space.
                      (RCRI 9050)
                                                                  U.S. TRUST COMPANY OF TEXAS, NATIONAL              
                                                                -----------------------------------------------------
                                                                Legal Title of Bank (TEXT 9010)

                                                                  2001 ROSS AVENUE, SUITE 2700                       
                                                                -----------------------------------------------------
                                                                City (TEXT 9130)

                                                                  DALLAS, TX  75201 
                                                                -----------------------------------------------------
                                                                State Abbrev. (TEXT 9200)        ZIP Code (TEXT 9220)

Board of Governors of the Federal Reserve System, Federal Deposit Insurance Corporation, Office of the Comptroller of the Currency


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U.S. TRUST COMPANY OF TEXAS, N.A.        Call Date: 12/31/96           STATE #  6797              FFIEC  034
2100 ROSS AVENUE, SUITE 2700             Vendor ID: D                  CERT: 33217                Page RC-1
DALLAS, TX 75201                         Transit Number: 11101765                 
                                                                                                   9

 
CONSOLIDATED REPORT OF CONDITION FOR INSURED COMMERCIAL
AND STATE-CHARTERED SAVINGS BANKS FOR DECEMBER 31, 1996
 
All schedules are to be reported in thousands of dollars. Unless otherwise
indicated, report the amount outstanding as of the last business day of the
quarter.
 
SCHEDULE RC - BALANCE SHEET    
 


                                                                                                                      C100 <-
                                                                                                  Dollar Amounts in Thousands
- -----------------------------------------------------------------------------------------------------------------------------
                                                                                                                
ASSETS                                                                                             RCON
                                                                                                   ----
  1. Cash and balances due from depository institutions:
     a.   Noninterest-bearing balances and currency and coin(1,2)...............................    0081          325    1.a
     b.   Interest bearing balances(3)..........................................................    0071          173    1.b
  2. Securities:
     a.   Held-to-maturity securities (from Schedule RC-B, column A)............................    1754            0    2.a
     b.   Available-for-sale securities (from Schedule RC-B, column D)..........................    1773      101,385    2.b
  3. Federal funds sold and securities purchased under agreements to resell:
     a.   Federal funds sold (4) ...............................................................    0276            0    3.a
     b.   Securities purchased under agreements to resell (5) ..................................    0277            0    3.b
  4. Loans and lease financing receivables:                                  RCON
                                                                             -----
     a.   Loans and leases, net of unearned income (from Schedule RC-C)...   2122         42,103                         4.a
     b.   LESS: Allowance for loan and lease losses.......................   3123            481                         4.b
     c.   LESS: Allocated transfer risk reserve...........................   3128              0                         4.c
     d.   Loans and leases, net of unearned income, allowance, and reserve (item 4.a minus 4.b      RCON
                                                                                                    ---
         and 4.c)..............................................................................     2125       41,622    4.d
  5. Trading assets ............................................................................    3545            0    5.
  6. Premises and fixed assets (including capitalized leases)...................................    2145          753    6.
  7. Other real estate owned (from Schedule RC-M)...............................................    2150            0    7.
  8. Investments in unconsolidated subsidiaries and associated companies (from Schedule
     RC-M)......................................................................................    2130            0    8.
  9. Customers' liability to this bank on acceptances outstanding...............................    2155            0    9.
 10. Intangible assets (from Schedule RC-M).....................................................    2143            0    10.
 11. Other assets (from Schedule RC-F)..........................................................    2160        1,511    11.
 12. a. Total assets (sum of items 1 through 11)................................................    2170      145,769    12.a
     b. Losses deferred pursuant to 12 U.S.C. 1823(j)...........................................    0306            0    12.b
     c. Total assets and losses deferred pursuant to 12 U.S.C. 1823 (j) (sum of items 12.a
        and 12.b)...............................................................................    0307      145,769    12.c


- ---------------
(1) Includes cash items in process of collection and unposted debits.
(2) The amount reported in this item must be greater than or equal to the sum
    of Schedule RC-M, items 3.a and 3.b 
(3) Includes time certificates of deposit not held for trading.
(4) Report 'term federal funds sold' in Schedule RC, item 4.a, 'Loans and
    leases, net of unearned income', and in Schedule RC-C, part 1.
(5) Report securities purchased under agreements to resell that involve the
    receipt of immediately available funds and mature in one business day or
    roll over under a continuing contract in Schedule RC, item 3.a, 'Federal
    funds sold.' 
    

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U.S. TRUST COMPANY OF TEXAS, N.A.      Call Date: 12/31/96             State: 6797                FFIEC  034
2100 ROSS AVENUE, SUITE 2700           Vendor ID: D                    CERT: 33217                Page RC-2
DALLAS, TX 75201                       Transit Number: 11101765                   
                                                                                                      10
                          

 
SCHEDULE RC -- CONTINUED
 


                                                                                          Dollar Amounts in Thousands
- ---------------------------------------------------------------------------------------------------------------------
                                                                                       RCON
                                                                                       ----
                                                                                                    
LIABILITIES
     Deposits:
13.  a. In domestic offices (sum of                                                   2200       118,129     13.a
        totals of columns A and C from Schedule RC-E.....          RCON
                                                                   ----
       (1) Noninterest-bearing(1)..................................6631        12,689                        13.a.1
       (2) Interest-bearing........................................6636       105,440                        13.a.2
     b. In foreign offices, Edge and Agreement subsidiaries, and IBFs
       (1) Noninterest-bearing.......................................................
       (2) Interest-bearing..........................................................
14.  Federal funds purchased and securities sold under agreements to repurchase:
     a. Federal funds purchased(2)................................................... 0278            0      14.a
     b. Securities sold under agreements to repurchase(3)............................ 0279            0      14.b
15.  a. Demand notes issued to the U.S. Treasury..................................... 2840            0      15.a
     b. Trading liabilities.......................................................... 3548            0      15.b
16.  Other borrowed money:
     a. With a remaining maturity of one year or less...............................  2332            0      16.a
     b. With a remaining maturity of more than one year.............................. 2333        6,000      16.b
17.  Mortgage indebtedness and obligations under capitalized leases.................  2910            0      17.
18.  Bank's liability on acceptances executed and outstanding.......................  2920            0      18.
19.  Subordinated notes and debentures..............................................  3200            0      19.
20.  Other liabilities (from Schedule RC-G).........................................  2930        1,575      20.
21.  Total liabilities (sum of items 13 through 20).................................  2948      125,704      21.
22.  Limited-life preferred stock and related surplus...............................  3282            0      22.
EQUITY CAPITAL
23.  Perpetual preferred stock and related surplus..................................  3838        7,000      23.
24.  Common stock...................................................................  3230          500      24.
25.  Surplus (exclude all surplus related to preferred stock).......................  3839        8,384      25.
26.  a. Undivided profits and capital reserves......................................  3632        4,045      26.a
     b. Net unrealized holding gains (losses) on available-for-sale securities......  8434          136      26.b
27.  Cumulative foreign currency translation adjustments............................  3210
28.  a. Total equity capital (sum of items 23 through 27)...........................  3210       20,065      28.a
     b. Losses deferred pursuant to 12 U.S.C. 1823 (j)..............................  0306            0      28.b
     c. Total equity capital and losses deferred pursuant to 12 U.S.C. 1823 (j)
        (sum of items 28.a and 28.b)................................................  3559       20,065      28.c
29.  Total liabilities, limited-life preferred stock, equity capital, and losses 
     deferred pursuant to U.S.C. 1823(j) (sum of items 21, 22 and 28.c).............  2257      145,769      29.

MEMORANDUM
TO BE REPORTED ONLY WITH THE MARCH REPORT OF CONDITION.
1. Indicate in the box at the right the number of the statement below that best    RCON           NUMBER
   describes the most comprehensive level of auditing work performed for the bank  ----
   by independent external auditors as of any date during 1995....................  6724           N/A     M.1

1 = Independent audit of the bank conducted in accordance with generally accepted auditing standards by a certified
    public accounting firm which submits a report on the bank
2 = Independent audit of the bank's parent holding company conducted in accordance with generally accepted auditing
    standards by a certified public accounting firm which submits a report on the consolidated holding company (but
    not on the bank separately)
3 = Directors' examination of the bank conducted in accordance with generally accepted auditing standards by a
    certified public accounting firm (may be required by state chartering authority)
4 = Directors' examination of the bank performed by other external auditors (may be required by state chartering
    authority)
5 = Review of the bank's financial statements by external auditors
6 = Compilation of the bank's financial statements by external auditors
7 = Other audit procedures (excluding tax preparation work)
8 = No external audit work

 
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(1) Includes total demand deposits and noninterest-bearing time and savings
    deposits.
(2) Report 'term federal funds purchased' in Schedule RC, item 16, 'Other
    borrowed money.'
(3) Report securities sold under agreements to repurchase that involve the
    receipt of immediately available funds and mature in one business day or
    roll over under a continuing contract in Schedule RC, item 14.a, 'Federal
    funds purchased.'