Exhibit 10.4

                              EMPLOYMENT CONTRACT

      THIS EMPLOYMENT CONTRACT (hereinafter referred to as this "Agreement"),
dated as of July 15, 2004, by and between GARY C. KELLY (hereinafter referred
to as the "Employee"), a resident of Dallas, Texas, and SOUTHWEST AIRLINES
CO. (hereinafter referred to as "Southwest", which term shall include its
subsidiary companies where the context so admits), a Texas corporation,

                             W I T N E S S E T H:
      WHEREAS the Employee has served as an executive officer of Southwest
for more than the past five years; and
      WHEREAS the Employee and Southwest desire to enter into an agreement
for the continuing full-time services of the Employee;
      NOW, THEREFORE, for and in consideration of the premises and the mutual
covenants and promises contained herein, Southwest and the Employee agree as
follows:

                     I.  POSITION, DUTIES AND AUTHORITY
A.    POSITIONS, DUTIES AND RESPONSIBILITIES.  The Employee shall serve as
      Chief Executive Officer of Southwest, and, for so long as he shall be
      elected to the Board of Directors of Southwest, he shall serve as Vice
      Chairman of the Board without additional compensation hereunder.  The
      Employee's duties and responsibilities as Chief Executive Officer shall
      include general oversight of the operational performance of Southwest;
      managing costs and generating revenues in order to achieve excellent
      financial performance; representing Southwest to its multitude of
      exterior constituencies; implementing Southwest's current and long
      range business policies and programs; handling, or overseeing, major
      contract negotiations; and, in general, maintaining employee morale and
      esprit de corps.  In addition, he shall perform such other corporate
      duties and discharge such other corporate responsibilities as are
      specified in the bylaws of Southwest or are] designated from time to
      time by either the Chairman of the Board of Directors of Southwest or
      the full Board of Directors.

B.    AUTHORITY.  The Employee shall be vested with all authority reasonably
      necessary to carry out his duties and responsibilities as set forth in
      this Article I.

C.    NECESSARY SUPPORT AND ENVIRONMENT.  The Employee shall be provided with
      the secretarial and other support personnel (including a full-time
      administrative assistant) and general working environment (including a
      private, furnished office) reasonably necessary for him to carry out
      his duties and responsibilities as set forth in this Article I.

                        II.  EMPLOYEE'S OBLIGATIONS

A.    TIME AND EFFORT.  During the term of his employment hereunder, the
      Employee shall devote such time and effort as is required to perform
      his duties and to discharge his responsibilities hereunder.  The
      Employee shall generally conform with all policies of Southwest as they
      apply to a person of his level of duties and responsibilities.

B.    NON-COMPETITION.  The Employee recognizes and understands that in
      performing the duties and responsibilities of his employment as
      outlined in this Agreement and pursuant to his employment at Southwest
      prior to the execution of this Agreement, the Employee has occupied and
      will occupy a position of trust and confidence, pursuant to which the
      Employee has developed and acquired and will develop and acquire
      experience and knowledge with respect to various aspects of the
      business of Southwest and the manner in which such business is
      conducted.  It is the expressed intent and agreement of the Employee
      and Southwest that such knowledge and experience shall be used in the
      furtherance of the business interests of Southwest and not in any
      manner which would be detrimental to such business interests of
      Southwest.  The Employee therefore agrees that, so long as the Employee
      is employed pursuant to this Agreement, unless he first secures the
      consent of the Board of Directors of Southwest, the Employee will not
      invest, engage or participate in any manner whatsoever, either
      personally or in any status or capacity (other than as a shareholder of
      less than one percent [1%] of the capital stock of a publicly owned
      corporation), in any business or other entity organized for profit
      engaged in significant competition with Southwest in the conduct of its
      air carrier operations anywhere in the States of Texas, Louisiana,
      Oklahoma, New Mexico, Missouri, Arizona, Nevada, California, Arkansas,
      Alabama, Tennessee, Kentucky, Michigan, Indiana, Ohio, Maryland,
      Illinois, Utah, Washington, Oregon, Nebraska, Florida, Idaho,
      Mississippi, New Hampshire, New York, Pennsylvania, Rhode Island,
      Connecticut, North Carolina and Virginia.  Although the Employee and
      Southwest regard such restrictions as reasonable for the purpose of
      preserving Southwest and its proprietary rights, in the event that the
      provisions of this Paragraph II-B should ever be deemed to exceed the
      time or geographic limitations permitted by applicable laws, then such
      provisions shall be reformed to the maximum time or geographic
      limitations permitted by applicable laws.

                                  III.  TERM

A.    TERM.  This Agreement and the Employee's employment hereunder shall
      commence and become effective on and as of July 15, 2004.  The term of
      such employment shall expire on July 15, 2007, unless extended by
      consent of the parties hereto or earlier terminated pursuant to the
      provisions of Article V.

                         IV.  EMPLOYEE'S COMPENSATION

A.    BASE SALARY.  The Employee's annual Base Salary for the years ending
      July 15, 2005, 2006 and 2007 shall be $399,722, $411,714 and $424,065,
      respectively.  The Employee's Base Salary shall be payable to the
      Employee in equal semi-monthly installments.  The Employee's Base
      Salary installment payments shall be subject to such payroll and
      withholding deductions as may be required by law.

B.    PERFORMANCE BONUS.  The Board of Directors of Southwest (or the
      Compensation Committee thereof) may grant a Performance Bonus to the
      Employee, in addition to his Base Salary, at such times and in such
      amounts as such Board (or Committee) may determine.

C.    DEFERRED COMPENSATION.  In addition to the Base Salary provided for in
      Paragraph IV-A above, Southwest shall set aside on its books a special
      ledger Deferred Compensation Account (the "Account") for the Employee,
      and shall credit thereto Deferred Compensation determined as
      hereinafter provided.  (Southwest at its election may fund the
      payment of Deferred Compensation by setting aside and investing such
      funds as Southwest may from time to time determine.  Neither the
      establishment of the Account, the crediting of Deferred Compensation
      thereto, nor the setting aside of any funds shall be deemed to
      create a trust.  Legal and equitable title to any funds set aside shall
      remain in Southwest, and the Employee shall have no security or other
      interest in such funds.  Any funds so set aside or invested shall
      remain subject to the claims of the creditors of Southwest, present and
      future.)  For each full or partial calendar year as the Employee shall
      remain in the employment of Southwest under this Agreement, Deferred
      Compensation shall accumulate in an amount equal to any contributions
      (including forfeitures but excluding any elective deferrals actually
      returned to the Employee) which would otherwise have been made by
      Southwest on behalf of the Employee to the Southwest Airlines Co.
      Profitsharing Plan but which exceed maximum annual additions under such
      Plan on his behalf under federal tax law.  If such employment shall
      terminate prior to December 31 in any calendar year, then Deferred
      Compensation shall accumulate and be calculated as provided under the
      terms of Southwest's Profitsharing Plan.  The Deferred Compensation
      credited to the Account (including the Interest hereinafter provided)
      shall be paid to the Employee (or to the executors or administrators of
      his estate) at the rate of $100,000 per calendar year (subject to such
      payroll and withholding deductions as may be required by law),
      commencing with the calendar year following the year in which (i) the
      Employee shall become sixty-five (65) or (ii) the Employee's employment
      with Southwest shall terminate (whether such termination is under this
      Agreement or otherwise and whether it is before, on or after the
      expiration of the initial term set forth in Paragraph III-A above, and
      irrespective of the cause thereof), whichever shall occur later, and
      continuing until the entire amount of Deferred Compensation and
      Interest credited to the Account shall have been paid.  Although the
      total amount of Deferred Compensation ultimately payable to the
      Employee hereunder shall be computed in accordance with the provisions
      set forth above, there shall be accrued and credited to the Account,
      beginning on January 1, 2005 and continuing annually thereafter,
      amounts equal to simple interest at the rate of ten percent (10%) per
      annum, compounded annually ("Interest"), on the accrued and unpaid
      balance of the Deferred Compensation credited to the Account as of the
      preceding December 31.  The Deferred Compensation and Interest to be
      paid in any one calendar year shall be paid on the first business day
      of such calendar year.  Notwithstanding the foregoing, in the event of
      the Employee's death, Southwest, in its sole discretion, shall have the
      right to pay the unpaid balance of the Deferred Compensation (together
      with any accrued Interest thereon) to the executors or administrators
      of the Employee's estate in cash in one lump sum on the first business
      day of the calendar year next following the calendar year in which the
      Employee shall have died.  No right, title, interest or benefit under
      this Paragraph IV-C shall ever be liable for or charged with any of the
      torts or obligations of the Employee or any person claiming under
      him, or be subject to seizure by any creditor of the Employee or any
      person claiming under him.  Neither the Employee nor any person
      claiming under him shall have the power to anticipate or dispose of any
      right, title, interest or benefit under this Paragraph IV-C in any
      manner until the same shall have been actually distributed by
      Southwest.

D.    DISABILITY INSURANCE.  Southwest shall provide long term disability
      insurance providing for payment, in the event of disability of the
      Employee, of $10,000 per month to age seventy (70).  Except as to
      amounts payable, the terms and conditions of such policy shall be
      identical, or substantially similar, to the disability insurance
      provided by Southwest for its other officers as of the date of this
      Agreement.

E.    MEDICAL AND DENTAL EXPENSES.  During the term of this Agreement, the
      Employee shall remain eligible to participate in any medical benefit
      plan or program that Southwest makes available to its employees
      generally. Upon termination of his employment with Southwest, the
      Employee shall be eligible to participate in any non-contract retiree
      medical benefit plan or program that Southwest may then make available
      to its retirees generally. Southwest shall reimburse the Employee for
      all his out-of-pocket expenses (including specifically all premiums and
      deductibles) that the Employee may incur for himself, his spouse and
      his children under any such Southwest plan or program during the
      term of this Agreement.

F.    STOCK OPTION GRANT.  Southwest shall grant to the Employee, effective
      as of the date hereof, ten-year non-qualified options to purchase
      180,000 shares of its common stock at a price per share equal to the
      fair market value thereof at the date hereof, with one-third of
      such options to be exercisable immediately and one-third to become
      exercisable on each of July 15, 2005 and July 15, 2006.

G.    OTHER BENEFITS.  The  Employee shall be eligible to continue to
      participate in all employee pension, profit-sharing, stock purchase,
      group insurance and other benefit plans or programs in effect for
      Southwest managerial employees generally to the extent of and in
      accordance with the rules and agreements governing such plans or
      programs, so long as same shall be in effect, with full service credit
      where relevant for the Employee's prior employment by Southwest.
      Southwest shall reimburse the Employee for reasonable expenses incurred
      by him in the performance of his duties and responsibilities hereunder.
      The Employee shall be entitled to vacation of three (3) weeks per year
      or such longer period as may be established from time to time by
      Southwest for its managerial employees generally.

                        V.   TERMINATION PROVISIONS

A.    EXPIRATION OR DEATH.  The Employee's employment hereunder shall
      terminate on July 15, 2007 (or such later date to which the term of
      this Agreement may be extended by consent of the parties hereto, in
      either case without prejudice to the Employee's privilege to
      remain an employee of Southwest thereafter), or upon the Employee's
      death, whichever shall first occur, without further obligation or
      liability of either party hereunder, except for Southwest's obligation
      to pay Deferred Compensation as provided in Paragraph IV-C of this
      Agreement.

B.    TERMINATION FOR CAUSE.  Southwest may terminate the Employee's
      employment hereunder upon the determination by a majority of its whole
      Board of Directors that the Employee has willfully failed and refused
      to perform his duties and to discharge his responsibilities hereunder.
      Such determination shall be final and conclusive.  If the Board of
      Directors of Southwest makes such determination, Southwest may (a)
      terminate the Employee's employment, effective immediately or at a
      subsequent date, or (b) condition his continued employment upon the
      circumstances and place a reasonable limitation upon the time within
      which the Employee shall comply with such considerations or
      requirements.  If termination is so effected, Southwest shall have no
      further liability to the Employee hereunder except for the obligation
      to pay Deferred Compensation as provided in Paragraph IV-C hereof.

C.    TERMINATION FOR DISABILITY.  Southwest may terminate the Employee's
      employment hereunder on account of any disabling illness, hereby
      defined to include any emotional or mental disorders, physical diseases
      or injuries as a result of which the Employee is, for a continuous
      period of ninety (90) days, unable to perform his duties and to
      discharge his responsibilities hereunder on a full-time basis.
      Southwest shall give to the Employee thirty (30) days' notice of its
      intention to effect such termination pursuant to this Paragraph V-C.
      If, within such notice period, the Employee shall have recovered from
      his disability sufficiently well to resume performance of his duties
      and discharge of his responsibilities on a full-time basis (although
      still undergoing treatment or rehabilitation), Southwest shall not have
      the right to effect such termination.  If such disabling illness occurs
      as a result of a job-related cause, Southwest shall continue to pay the
      Employee regular installments of his Base Salary in effect at the time
      of such termination for the remainder of the term of this Agreement.
      It is expressly understood and agreed, however, that any obligation of
      Southwest to continue to pay the Employee his Base Salary pursuant to
      this Paragraph V-C shall be reduced by the amount of any proceeds of
      long-term disability insurance provided for the Employee pursuant to
      Paragraph IV-D above, and shall also be reduced by the amount of the
      proceeds of any worker's compensation or other benefits which the
      Employee receives as a result of or growing out of his disabling
      illness.

D.    CHANGE OF CONTROL TERMINATION.  In the event of any change of control
      of Southwest, the Employee may, at his option, terminate his employment
      hereunder by giving to Southwest notice thereof no later than sixty
      (60) days after the Employee shall have determined or ascertained that
      such change has occurred, irrespective whether Southwest shall have
      purported to terminate this Agreement after such event but prior to
      receipt of such notice.  If termination is so effected, no later than
      the date of such termination Southwest shall pay the Employee as
      "severance pay" a lump sum equal to (i) $750,000 plus (ii) an amount
      equal to the unpaid installments of his Base Salary in effect at the
      time of such termination for the remaining term of this Agreement.  If
      termination is so effected, Southwest shall have no other further
      liability to the Employee hereunder except for its obligation to pay
      Deferred Compensation as provided in Paragraph IV-C above.  For
      purposes of this Paragraph V-D, a "change of control of Southwest"
      shall be deemed to occur if (i) a third person, including a "group" as
      determined in accordance with Section 13(d)(3) of the Securities
      Exchange Act of 1934, becomes the beneficial owner of shares of
      Southwest having twenty percent (20%) or more of the total number of
      votes that may be cast for the election of directors of Southwest, or
      (ii) as a result of, or in connection with, any cash tender or exchange
      offer, merger or other business combination, sale of assets or
      contested election, or any combination of the foregoing transactions
      (herein called a "Transaction"), the persons who were directors of
      Southwest before the Transaction shall cease to constitute a majority
      of the Board of Directors of Southwest or any successor to Southwest.

E.    VOLUNTARY TERMINATION.  The Employee's employment hereunder shall
      terminate forthwith upon his resignation and its acceptance by
      Southwest, without further obligation or liability of either party
      hereunder, except for Southwest's obligation to pay Deferred
      Compensation as provided in Paragraph IV-C above.

                            VI.  MISCELLANEOUS

A.    ASSIGNABILITY, ETC.  The rights and obligations of Southwest hereunder
      shall inure to the benefit of and shall be binding upon the successors
      and assigns of Southwest; provided, however, Southwest's obligations
      hereunder may not be assigned without the prior approval of the
      Employee.  This Agreement is personal to the Employee and may not be
      assigned by him.

B.    NO WAIVERS.  Failure to insist upon strict compliance with any
      provision hereof shall not be deemed a waiver of such provision or any
      other provision hereof.

C.    AMENDMENTS.  This Agreement may not be modified except by an agreement
      in writing executed by the parties hereto.

D.    NOTICES.  Any notice required or permitted to be given under this
      Agreement shall be in writing in the English language and shall be
      deemed to have been given to the person affected by such notice when
      personally delivered or when deposited in the United States mail,
      certified mail, return receipt requested and postage prepaid, and
      addressed to the party affected by such notice at the address indicated
      on the signature page hereof.

E.    SEVERABILITY.  The invalidity or unenforceability of any provision
      hereof shall not affect the validity or enforceability of any other
      provision hereof.

F.    COUNTERPARTS.  This Agreement may be executed in multiple counterparts,
      each of which shall be deemed an original but all of which taken
      together shall constitute a single instrument.

G.    ENTIRE AGREEMENT.  This Agreement contains all of the terms and
      conditions agreed upon by the parties hereto respecting the subject
      matter hereof, and all other prior agreements, oral or otherwise,
      regarding the subject matter of this Agreement shall be deemed to be
      superseded as of the date of this Agreement and not to bind either of
      the parties hereto.

H.    GOVERNING LAW.  This Agreement shall be subject to and governed by the
      laws of the State of Texas.

      IN WITNESS WHEREOF, the Employee has set his hand hereto and Southwest
has caused this Agreement to be signed in its corporate name and behalf by
one of its officers thereunto duly authorized, all as of the day and year
first above written.

                                   SOUTHWEST AIRLINES CO.



                                   By: /s/ Herbert D. Kelleher
                                           Herbert D. Kelleher
                                           Chairman of the Board of Directors






                                   THE EMPLOYEE



                                       /s/ Gary C. Kelly
                                           Gary C. Kelly

                                           Address:  P.O. Box 36611
                                           Dallas, Texas  75235-1611