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                                                                     EXHIBIT 4.9
                   FIRST AMENDMENT TO PARTICIPATION AGREEMENT
                            Dated as of May 1, 1998
                                     among
                            SOUTHWEST AIRLINES CO.,
                                   as Lessee
                        CHRYSLER FINANCIAL CORPORATION,
                              as Owner Participant
                           FIRST UNION NATIONAL BANK,
       in its individual capacity only as expressly provided herein and
                      otherwise solely as Owner Trustee,
                                       and
                           WILMINGTON TRUST COMPANY,
              in its individual capacity and as Indenture Trustee
               and in its capacity as Pass Through Trustee under
                        the Pass Through Trust Agreement
                                 and as Holder
                       One Boeing Model 737-3H4 Aircraft
                     (Southwest Airlines 1996 Trust N620SW)
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                   FIRST AMENDMENT TO PARTICIPATION AGREEMENT
         THIS FIRST AMENDMENT TO PARTICIPATION AGREEMENT dated as of May 1,
1998 (this "Amendment") by and among (i) Southwest Airlines Co., a Texas
corporation ("Lessee"), (ii) Chrysler Financial Corporation, a Michigan
corporation ("Owner Participant"), (iii) First Union National Bank, a national
banking association, not in its individual capacity, except as expressly
provided herein, but solely as Owner Trustee under the Trust Agreement ("Owner
Trustee"), and (iv) Wilmington Trust Company, a Delaware banking corporation,
in its individual capacity and as Indenture Trustee under the Trust Indenture
(the "Indenture Trustee") and in its capacity as Pass Through Trustee under the
Pass Through Trust Agreement ("Pass Through Trustee") and as Holder, amends
that certain Participation Agreement respecting the aircraft having U.S.
registration number N620SW and dated as of June 1, 1996 (the "Participation
Agreement"), by and among Lessee, Owner Participant, Royal Bank of Canada, a
Canadian chartered bank, acting through its New York Branch (the "Original Loan
Participant"), Owner Trustee and Indenture Trustee,
                                  WITNESSETH:
         WHEREAS, except as otherwise defined in this Amendment, capitalized
terms used herein shall have the meanings attributed thereto in the
Participation Agreement; and
         WHEREAS, the Delivery Date occurred on June 3, 1996; and
         WHEREAS, concurrently with the execution of this Amendment, the Series
SWA 1996 Trust N620SW-I Certificate held by the Original Loan Participant is
being refinanced by the issuance of one or more new Certificates issued to Pass
Through Trustee as Holder; and
         WHEREAS, as contemplated by Section 18 of the Participation Agreement,
the parties hereto desire to amend the Participation Agreement in certain
respects;
         NOW, THEREFORE, in consideration of the mutual agreements herein
contained, the parties hereto agree as follows:
         Section 1.       Amendment to Schedule I.  Schedule I to the
Participation Agreement is hereby deleted in its entirety and replaced with
Schedule I to this Agreement.
         Section 2.       Amendments to Section 7(b).  Section 7(b) of the
Participation Agreement is hereby amended in the following manner:
                 (i)      Section 7(b) is hereby amended such that wherever the
phrase "Operative Agreement" or "Operative Agreements" is used, such phrase is
hereby amended to be and read in its entirety as follows:
                 "Operative Agreement or Pass Through Trust Agreement" and
                 "Operative Agreements or Pass Through Trust Agreement"
                        PARTICIPATION AMENDMENT [N620SW]
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except in the case of Section  7(b)(iii) where the phrase "Operative
Agreements" is hereby amended to be and read, in its entirety, "Operative
Agreements and the Pass Through Trust Agreement."
                 (ii)     Section 7(b)(i) is hereby amended as follows:
                 (a) the following language is added immediately after the
                 words "combined or unitary return with such Indemnified
                 Party)" and before the words "harmless from, any and all":
                 "except that for purposes of this Section 7(b)(i) an
                 Indemnified Party shall not include any Holder other than
                 Original Loan Participant";
                 (b) unless as otherwise provided in (c) below, wherever the
                 term "Certificates" is used, such term is hereby amended to be
                 and read in its entirety as follows:
                 "Certificates and each Pass Through Certificate"; and
                 (c) the language immediately after the phrase "or the
                 issuance, reissuance, acquisition, redemption, expiration or
                 subsequent transfer thereof under the Trust Indenture" is
                 hereby amended to be and read in its entirety as follows:
                 "and the Pass Through Trust Agreement, or the beneficial
                 interests in the Trust Estate and the Pass Through Trust
                 Estate or the creation thereof, or any payments made pursuant
                 to any such agreement or instrument or upon or with respect to
                 the property held by Owner Participant or by the Trust Estate
                 or by Indenture Trustee under the Trust Indenture or the
                 property held by Pass Through Trustee under the Pass Through
                 Trust Estate, amounts payable with respect to the Certificates
                 and each Pass Through Certificate, including withholding Taxes
                 imposed on payments of principal, interest, Premium or Break
                 Amount on the Certificates or payments of principal of,
                 interest on or any other amounts payable with respect to each
                 Pass Through Certificate that are asserted against the Owner
                 Participant, Owner Trustee or Pass Through Trustee, as
                 withholding agent, or otherwise with respect to or in
                 connection with the transactions contemplated by the Operative
                 Agreements."
         Section 3.       Amendments to Section 7(c).  Section 7(c) of the
Participation Agreement shall be amended in the following manner:
                 (i)      Section 7(c) is hereby amended such that wherever the
phrase "Operative Agreement" or "Operative Agreements" is used, such phrase
includes the Pass Through Trust Agreement.
                 (ii)     Clause (d) of Section 7(c)(i) is hereby amended to be
and read in its entirety as follows:
                 "(d) the offer, sale or delivery of the Certificates or the
                 Pass Through Certificates, whether before or after the
                 Delivery Date (the indemnity in this clause (d) to extend
                        PARTICIPATION AMENDMENT [N620SW]
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                 also to any Person who controls an Indemnified Party, its
                 successors, assigns, employees, servants and agents within the
                 meaning of Section 15 of the Securities Act)."
                 (iii)    The final paragraph of Section 7(c) is hereby amended
to be and read in its entirety as follows:
                 "Lessee agrees to pay the reasonable and continuing fees and
                 expenses of Indenture Trustee (including the reasonable fees
                 and expenses of its counsel and any agent appointed in
                 accordance with Section 9.02(c) of the Trust Indenture) and
                 Pass Through Trustee and, as provided in Section 6.07 of the
                 Trust Agreement, Owner Trustee (including, but not limited to,
                 the reasonable fees and expenses of its counsel), without
                 cost, on a net after-tax basis, to Owner Participant, for
                 acting as such, other than such fees and expenses which
                 constitute Transaction Costs and are payable by Owner
                 Participant under Section 16.  Lessee agrees that it will pay
                 the reasonable fees and expenses of any separate owner trustee
                 or co-trustee appointed pursuant to Section 9.02 of the Trust
                 Agreement as a result of any requirement of law or if
                 otherwise required by any Operative Agreement or if requested,
                 or consented to, by Lessee."
         Section 4.       Amendments to Section 8.  Section 8 of the
Participation Agreement is hereby amended in the following respects:
                 (i)      Section 8(e) is hereby amended to be and read in its
entirety as follows:
                 "(e)     (i)  Pass Through Trustee hereby agrees that, except
                 as otherwise required by applicable law including, without
                 limitation, any law which requires Pass Through Trustee to act
                 within its own discretion, it shall not, without the prior
                 written consent of Owner Trustee, direct Indenture Trustee to
                 take or refrain from taking any action under the Trust
                 Indenture that requires the approval, waiver, authorization,
                 direction or consent of, or notice from, the Holders holding a
                 specified percentage in principal amount of Outstanding (as
                 defined in the Trust Indenture) Certificates unless Pass
                 Through Trustee receives a Direction (as defined in the Pass
                 Through Trust Agreement) to so direct the Indenture Trustee
                 from Certificateholders (as defined in the  Pass Through Trust
                 Agreement) holding the same percentage in principal amount of
                 Outstanding Certificates (as defined in the Pass Through Trust
                 Agreement) evidencing Fractional Undivided Interests (as
                 defined in the Pass Through Trust Agreement) in the Trust (as
                 defined in the Pass Through Trust Agreement) holding the
                 Certificates.
                          (ii)  Lessee and Pass Through Trustee hereby agree
                 that Article X of the Pass Through Trust Agreement (to the
                 extent relating to the Certificates) shall not be amended
                 without the prior written consent of Owner Participant.
                          (iii)  Pass Through Trustee hereby agrees that,
                 except as otherwise required by applicable law including,
                 without limitation, any law which requires Pass Through
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                 Trustee to act within its own discretion, if requested to do
                 so by Owner Trustee or Owner Participant, Pass Through Trustee
                 shall request a Direction from the relevant Certificateholders
                 to establish whether Pass Through Trustee, in its capacity as
                 a Holder, may direct the Indenture Trustee to take or refrain
                 from taking any action under the Operative Agreements."
                 (ii)     Section 8(l) is hereby amended by deleting the
references therein to the Original Loan Participant.
                 (iii)    Section 8(bb) is hereby amended to be and read in its
entirety as follows:
                 "(bb)    Transfers of Debt Interests.  Except in connection
                 with any transfer pursuant to Section 17 or 18 hereof, or
                 Section 8.03(e)(ii) of the Indenture, each Holder covenants
                 that it will not transfer its Certificate to any Person unless
                 such Person represents and warrants in writing to such Holder,
                 the Owner Participant and Lessee either that (a) no part of
                 the funds used by it to acquire its Certificate constitutes
                 'plan assets' of any 'employee benefit plan' within the
                 meaning of ERISA or any 'plan' within the meaning of Section
                 4975(e)(1) of the Code or (b) its purchase or acquisition of
                 such Certificate will not result in a nonexempt prohibited
                 transaction under Section 4975 of the Code or Section 406 of
                 ERISA.  Any such Person shall require any transferee of its
                 interest to make the representations and warranties in the
                 preceding sentence."
         Section 5.       Amendments to Section 11(f).  Section 11(f) of the
Participation Agreement is hereby amended such that wherever the phrase
"Operative Agreement" or "Operative Agreements" is used, such phrase is hereby
amended to be and read in its entirety as follows:
                 "Operative Agreement and the Pass Through Trust Agreement" and
                 "Operative Agreements and the Pass Through Trust Agreement."
         Section 6.       Amendments to Section 15.  Section 15(b) of the
Participation Agreement is hereby amended to be and read in its entirety as
follows:
                 "(b)     Survival.  The representations, warranties,
                 indemnities and agreements of Lessee, Owner Trustee, Indenture
                 Trustee, Owner Participant, Pass Through Trustee and any
                 Holder provided for in this Agreement, and Lessee's, Owner
                 Trustee's, Indenture Trustee's, Owner Participant's, Pass
                 Through Trustee's and any Holder's obligations under any and
                 all thereof, shall survive the making available of the Owner
                 Participant's Commitment, the delivery or return of the
                 Aircraft, the transfer of any interest of Owner Participant in
                 the Trust Estate or the Aircraft or any Engine or the transfer
                 of any interest by any Holder in any Certificate or the Trust
                 Indenture Estate and the expiration or other termination of
                 this Agreement, any other Operative Agreement or the Pass
                 Through Trust Agreement, except as otherwise expressly
                 provided herein or therein."
                        PARTICIPATION AMENDMENT [N620SW]
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         Section 7.       Amendment to Section 16.  Section 16(b) of the
Participation Agreement is hereby amended by changing "0.327156%" in clause (i)
thereof to read "0.332897%" and by changing "0.641933%" in clause (ii) thereof
to read "0.643305%."
         Section 8.       Ratification.  Except as amended hereby, the
Participation Agreement continues and shall remain in full force and effect in
all respects.
         Section 9.       Authorization to Execute Amendments.  By execution of
this Amendment, Owner Participant hereby authorizes, directs and instructs
Owner Trustee to execute and deliver this Amendment and any and all other
amendments, agreements and certificates as may be necessary as a result of the
refinancing contemplated hereby and by Section 18 of the Participation
Agreement.
         Section 10.      Pass Through Trustee a Party.  Effective as of the
date hereof, Pass Through Trustee shall be a party to the Participation
Agreement and shall have the rights and obligations of the Holders as set forth
in the Participation Agreement, as amended hereby.
         Section 11.      Counterparts.  This Amendment may be executed by the
parties hereto in separate counterparts, each of which when so executed and
delivered shall be an original, but all such counterparts shall together
constitute but one and the same instrument.
         Section 12.      Governing Law.  THIS AMENDMENT SHALL IN ALL RESPECTS
BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE INTERNAL LAWS OF THE
STATE OF NEW YORK.  THIS AMENDMENT IS BEING DELIVERED IN THE STATE OF NEW YORK.
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         IN WITNESS WHEREOF, the parties hereto have caused this First
Amendment to Participation Agreement to be duly delivered in the State of New
York and executed by their respective officers thereunto duly authorized as of
the day and year first above written.
                                SOUTHWEST AIRLINES CO., Lessee
                                By:                                     
                                   -------------------------------------
                                         Treasurer
                                CHRYSLER FINANCIAL CORPORATION
                                    Owner Participant
                                By:                                     
                                   -------------------------------------
                                         Vice President
                                FIRST UNION NATIONAL BANK,
                                    in its individual capacity only as
                                    expressly provided herein and
                                    otherwise solely as Owner Trustee
                                By:                                    
                                   ------------------------------------
                                         Corporate Trust Officer
                                WILMINGTON TRUST COMPANY,
                                    not in its individual capacity,
                                    except as otherwise expressly
                                    provided herein, but solely as
                                    Indenture Trustee
                                By:                                    
                                   ------------------------------------
                                         Senior Financial Services Officer
                                WILMINGTON TRUST COMPANY,
                                    in its capacity as Pass Through
                                    Trustee under each of the
                                    separate Pass Through Trust
                                    Agreements and as Holder
                                By:                                       
                                   ---------------------------------------
                                         Senior Financial Services Officer
                        PARTICIPATION AMENDMENT [N620SW]
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                                   SCHEDULE I
                              Names and Addresses
                                                     
Lessee:                                                 Indenture Trustee and Pass Through      
                                                        Trustee and Holder:                     
Southwest Airlines Co.                                                                          
▇▇▇▇ ▇▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇                                   ▇▇▇▇▇▇▇▇▇▇ Trust Company                
▇.▇. ▇▇▇ ▇▇▇▇▇                                          ▇▇▇▇▇▇ ▇▇▇▇▇▇ ▇▇▇▇▇                     
▇▇▇▇▇▇, ▇▇▇▇▇ ▇▇▇▇▇-▇▇▇▇                                ▇▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇▇ ▇▇▇▇▇▇                
▇▇▇▇:  Treasurer                                        ▇▇▇▇▇▇▇▇▇▇, ▇▇▇▇▇▇▇▇ ▇▇▇▇▇-▇▇▇▇         
Telecopy: (▇▇▇) ▇▇▇-▇▇▇▇                                                                        
                                                        Attn:  Corporate Trust                  
Payment Instructions:                                   Administration                          
Southwest Airlines Co.                                  Telecopy:  (▇▇▇) ▇▇▇-▇▇▇▇               
Bank One Dallas                                                                                 
ABA No. 11100614                                        Payment Instructions:                   
Account No.  ▇▇▇▇▇▇▇▇                                   Wilmington Trust Company                
Reference:  ▇▇▇▇▇▇                                      ▇▇▇▇▇▇▇▇▇▇, ▇▇▇▇▇▇▇▇                    
                                                        ABA No. ▇▇▇▇▇▇▇▇▇                       
Owner Participant:                                      For the account of Southwest            
                                                         Airlines 1996-1                        
Chrysler Financial Corporation                          Account No. 30875-0                     
225 High Ridge Road                                     Reference:  ▇▇▇▇▇▇                      
▇▇▇▇▇▇▇▇, ▇▇  ▇▇▇▇▇                                     Attn:    ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇              
Telecopy:  (▇▇▇) ▇▇▇-▇▇▇▇                                        Corporate Trust Administration 
                                                                                                
Payment Instructions:                                                                           
The Chase Manhattan Bank                                                                        
ABA No. ▇▇▇▇▇▇▇▇▇                                                                               
For the account of                                                                              
Chrysler Financial Corporation                                                                  
Account No. ▇▇▇-▇-▇▇▇▇▇▇
Reference:  Southwest Airlines
Owner Trustee:
First Union National Bank
▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇▇, ▇▇▇ ▇▇▇▇▇
▇▇▇▇▇▇▇▇▇, ▇▇  ▇▇▇▇▇-▇▇▇▇
Attn:  Bond Administration
Telecopy:  (▇▇▇) ▇▇▇-▇▇▇▇
Payment Instructions:
First Union National Bank
▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇▇, ▇▇▇ ▇▇▇▇▇
▇▇▇▇▇▇▇▇▇, ▇▇  ▇▇▇▇▇-▇▇▇▇
ABA No. ▇▇▇▇▇▇▇▇▇
Account No. 465946
Attn:  Bond Administration/Pablo de la Canal
Reference:  Southwest Airlines
                                        
                        PARTICIPATION AGREEMENT [N620SW]
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