<PAGE>

                                                                    EXHIBIT 10.4

                           [LETTERHEAD APPEARS HERE]

                                  July 7, 1999

Mr. Karim Alibhai
10777 Westheimer
Suite 1000
Houston, TX 77042

Dear Karim:

     This letter agreement (the "Agreement") confirms the agreement that we have
reached regarding your resignation from your regular, full-time employment and
all offices you held with Wyndham International, Inc. ("WII") and its related
and affiliated entities (collectively, "Wyndham").

     This Agreement does not constitute and should not be construed as an
admission by Wyndham or Patriot American Hospitality, Inc. ("PAHI") and its
related and affiliated entities (collectively with PAHI, "Patriot") (Wyndham and
Patriot, collectively hereinafter referred to as the "Companies") that they have
in any way violated any legal obligation that they owe to you or to any other
person or as an admission by you that you have in any way violated any legal
obligation that you owe to the Companies or to any other person. To the
contrary, the parties' willingness to enter into this Agreement demonstrates
that they are continuing to deal with each other fairly and in good faith.

     With those understandings and in exchange for the promises set forth below,
you and the Companies agree as follows:

     1.   Resignation
          -----------

     You hereby confirm that you resigned as an employee of WII effective as of
June 30, 1999 (the "Resignation Date"). You also hereby confirm that you
resigned from your offices of President and Chief Operating Officer of WII and
any and all employment, offices and board of directors seats (other than your
directorship on WII's Board) that you held with any of the other Companies as of
the Resignation Date. The Companies hereby confirm that said resignations were
accepted by the Companies.

     WII agrees to nominate you as a Class 3 Director for the Board of Directors
of WII ("Board") in connection with the merger of WII and PAHI. In the event
that the Board establishes and delegates certain of its authority to an
executive committee of the
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 2


Board, WII shall recommend and support your candidacy for a seat on such
committee to the extent that the structure of such a committee so permits.

     2.   Compensation and Benefit
          ------------------------

          (a)  Repricing of Outstanding Options. As of June 1, 1999, all of your
               --------------------------------
outstanding options to purchase 601,065 paired shares of the common stock of WII
and PAHI ("Paired Shares") hereby are canceled, and in lieu thereof you are
granted fully vested new options to purchase 100,000 shares of common stock of
WII (formerly denominated as Paired Shares) at a purchase price of $5. 1875 per
share (the "New Options"). The New Options shall remain fully exercisable until
June 30, 2002 and otherwise shall remain subject to the terms of paragraphs
2(c), 2(d), 7, 8, 9, 11, 12, and 14 of the Patriot American Hospitality
Operating Company Non-Qualified Stock Option Agreement dated as of June 12, 1998
by and between you and PAHI.

          (b)  Pro Rata Bonus. The Companies agree to pay you, on or within a
               --------------
reasonable time after the annual compensation determination date established by
the Board, a lump sum of One Hundred Eighty-Thousand Dollars ($180,000) as a pro
rata incentive bonus for 1999.

          (c)  Benefit Continuation. You may continue to participate in WII's
               --------------------
group health, dental, life and disability insurance plans in which, and to the
same extent as, you are currently participating for up to two (2) years from the
Resignation Date, with the cost of the regular premium for such benefits shared
in the same relative proportion by you and WII as in effect for senior
executives of WIT on the Resignation Date; provided that nothing in this Section
                                           --------
2(c) shall be construed to affect your or your dependents' rights thereafter (i)
to receive continuation coverage to the extent authorized by and consistent with
29 U.S.C. (S) 1161 et seq. (commonly known as "COBRA") and applicable group
health and dental plan terms, or (ii) convert your coverage under the life and
disability plans to individual coverage to the extent authorized by and
consistent with applicable group life and disability plan terms, in all cases
entirely at your or their own cost after your right to cost sharing under this
Section 2(c) ends.

          (d)  Office. WII shall continue to provide you with the use of one
               ------
support staff member through December 31, 1999 (Natalie Dixon to the extent she
remains employed by WII). WII shall make a suitable office at its corporate
headquarters available to the assigned support staff member through December 31,
1999.
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 3


          (e)  Hotel Suite. WII shall make Suite 1013 at the Grand Bay Miami
               -----------
available to you for your use through November 21, 1999.

          (f)  Other Benefits. Except as expressly provided above, your
               --------------
eligibility to participate in any of the Companies' respective employee benefit
plans and programs ceases on or after the Resignation Date in accordance with
the terms and conditions of each of those benefit plans and programs and your
rights to benefits under any of the employee benefit plans and programs, if any,
are governed by the terms and conditions of each of those employee benefit plans
and programs.

     3.   Release of Claims
          -----------------

          (a)  Release by Mr. Alibhai. You voluntarily and irrevocably release
               ----------------------
and discharge the Companies, their related or affiliated entities, and their
respective predecessors, successors, and assigns, and, solely in their
respective capacities as such, the current and former officers, directors,
shareholders, employees, and agents of each of the foregoing (any and all of
which are referred to as "Releasees") generally from all charges, complaints,
claims, promises, agreements, causes of action, damages, and debts that relate
in any manner to your employment with or services as an employee for the
Companies, known or unknown ("Claims"), which you have, claim to have, ever had,
or ever claimed to have had against any of the Releasees through the date on
which you execute this Agreement. This general release of Claims includes,
without implication of limitation, all Claims for or related to: the Employment
Agreement; the compensation provided to you by the Companies; your resignations
as described in Section 1; wrongful or constructive discharge; breach of
contract; breach of any implied covenant of good faith and fair dealing;
tortious interference with advantageous relations; intentional or negligent
misrepresentation, fraud or deceit; infliction of emotional distress, and
unlawful discrimination under the common law or any statute (including, without
implication of limitation, the Employee Retirement Income Security Act, Title
VII of the Civil Rights Act of 1964, the American with Disabilities Act, Tex.
Lab. Code (S) 21.001, et seq., and Tex. Hum. Res. Code (S) 121.001, et seq.).
You also waive any Claim for reinstatement, severance, incentive or retention
pay (except as expressly provided in this Agreement), attorney's fees, or costs,
relating to the Claims.

     You agree that you will not hereafter pursue any Claim against any Releasee
by filing a lawsuit in any local, state or federal court for or on account of
anything which has occurred up to the date on which you execute this Agreement
as a result of your employment, and you shall not seek reinstatement with, or
damages of any nature, severance, incentive or retention pay, attorney's fees,
or costs from the Companies or any of the other Releasees; provided, however,
                                                           --------
that nothing in this general release shall
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 4


be construed to bar or limit your rights, if any, to indemnification subject to
and in accordance with the terms of the By-Laws of WII and the Indemnification
Agreement, dated as of May 23, 1998, by and among you, WII and PAHI (the
"Indemnification Agreement"), or to enforce your rights under this Agreement.

          (b)  Release by the Companies. The Companies, on behalf of themselves
               ------------------------
and their respective predecessors, successors, assigns, directors (but only in
their capacities as directors of the Companies) and officers (but only in their
capacities as officers of the Companies) voluntarily and irrevocably release and
discharge you and your successors, assigns, heirs and survivors from any and all
charges, complaints, claims, promises, agreements, causes of action, damages and
debts (including attorney's fees and costs actually incurred) which any of them
have, claim to have, ever had or ever claimed to have had against you through
the date hereof, that are known to the Companies or that presently are not
actually known to senior management of the Companies but that directly or
indirectly arise out of, relate to or concern good faith acts or omissions by
you during the course of your employment undertaken or not undertaken in the
reasonable belief that such acts or omissions were in or not opposed to the best
interests of the Companies ("WII Claims").

     The Companies further represent that they do not have any knowledge at this
time of any acts or omissions by you that would give rise claims not otherwise
released in the previous paragraph.

     4.   Employment Agreement
          --------------------

     This Agreement supersedes all provisions of the Employment Agreement other
than Paragraphs 4, 5 (as amended and restated hereinbelow), 8(c), 13 and 15
thereof. Paragraphs 4, 5 (as amended and restated hereinbelow), 8(c), 13 and 15
of the Employment Agreement are incorporated herein by reference and shall
continue to bind you in accordance with their respective terms. The parties
hereby agree that Paragraph 5 of the Employment Agreement, however, is
incorporated herein only to the extent amended and restated as follows:

     The provisions of this Paragraph 5 shall apply during Executive's
     employment with the Company and for a period of twelve (12) months
     thereafter. In consideration for Executive's employment by the Company
     under the terms provided in this Agreement and as a means to aid in the
     performance and enforcement of the terms of the Unauthorized Disclosure
     provisions of Paragraph 4, Executive agrees that Executive will not,
     directly or indirectly, solicit or induce any present or future employee of
     the Company or Affiliated Company to accept employment with Executive or
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 5


     with any business, operation, corporation, partnership, association,
     agency, or other person or entity with which Executive may be associated,
     and Executive will not employ or cause any business, operation,
     corporation, partnership, association, agency, or other person or entity
     with which Executive may be associated to employ any present or future
     employee of the Company or Affiliated Company without providing the Company
     or Affiliated Company with ten (10) days' prior written notice of such
     proposed employment. Should Executive violate the provisions of this
     Paragraph 5, then in addition to all other rights and remedies available to
     the Company or Affiliated Company at law or in equity, the duration of this
     covenant shall automatically be extended for the period of time from which
     Executive began such violation until he permanently ceases such violation.

     The parties further agree that Paragraph 8(c) (Gross Up Payment) of the
Employment Agreement shall be applied with respect to the payments to you under
this Agreement if such payments results in an Excise Tax (as defined in the
Employment Agreement).

     The Employment Agreement, except for Paragraphs 4, 5 (as amended and
restated herein), 8(c), 13 and 15 thereof, shall terminate on the Resignation
Date.

     5.   Return of Property
          ------------------

     All documents, records, material and all copies of any of the foregoing
pertaining to Confidential Information (as defined in Paragraph 4 of the
Employment Agreement), and all software, equipment, and other supplies, whether
or not pertaining to Confidential Information, that have come into your
possession or been produced by you in connection with your employment
("Property") have been and remain the sole property of the Companies. You
confirm that you have returned all Property to the Companies, except for the
notebook computer currently in your possession. The Companies agree that you may
keep the notebook computer, so long as you first permit the Companies to remove
any Confidential Information from it. In no event should this provision be
construed to require you to return to the Company any document or other
materials concerning your remuneration and benefits during your employment with
the Companies. The Companies agree to return to you, promptly upon your request,
such of your property as may be in the possession of any of the Companies.
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 6


     6.   Nondisparagement
          ----------------

     You agree not to take any action or make any statement, written or oral,
which disparages or criticizes the Companies or their respective officers,
directors, agents, or management and business practices, or which disrupts or
impairs the Companies' normal operations. The Companies, on behalf of
themselves, agree (a) not to take any action or make any statement, written or
oral, which disparages or criticizes you or your management and business
practices, and (b) to instruct their respective directors and officers not to
take any action or make any statement, written or oral, which disparages or
criticizes you or your management and business practices. The provisions of this
Section 6 shall not apply to any truthful statement required to be made by you
or the Companies, as the case may be, in any legal proceeding or governmental or
regulatory investigation.

     You shall be entitled to review and approve, which approval shall not be
unreasonably withheld, the content of any press release or other public
statement issued by the Companies concerning your resignation and participate in
the transaction call announcing your resignation.

     7.   Additional Representations. Warranties and Covenants
          ----------------------------------------------------

          (a)  As a material inducement to the Companies to enter into this
Agreement, you represent, warrant and covenant as follows:

          (i)  You have not assigned to any third party any Claim released by
     this Agreement.

          (ii) You have not heretofore filed with any agency or court any Claim
     released by this Agreement.


          (b)  As a material inducement to you to enter into this Agreement, the
Companies represent, warrant and covenant as follows:

          (i)  The Companies have not assigned to any third party any WII
          Claims released by this Agreement; and

          (ii) The Companies have not heretofore filed with any agency or court
          any WII Claims released by this Agreement.
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 7


     8.   Further Assurances
          ------------------

     Upon the terms and subject to the conditions herein provided, each of the
parties hereto agrees to use its reasonable efforts to take, or cause to be
taken, all action and to do, or cause to be done, all things necessary, proper
or advisable under applicable laws and regulations to consummate and make
effective the transactions contemplated by this Agreement.

     9.   Exclusivity
          -----------

     This Agreement sets forth all the consideration to which you are entitled
from the Companies by reason of your resignation and the consummation by the
Companies of any strategic restructuring or transaction, and you shall not be
entitled to or eligible for any payments or benefits under any other Company
severance, bonus, retention or incentive policy, arrangement or plan.

     10.  Tax Matters
          -----------

     All payments and other consideration provided to you pursuant to this
Agreement shall be subject to any deductions, wititholding or tax reporting that
the Companies reasonably determine to be required for tax purposes.

     11.   Acknowledgment
           --------------

     WII hereby acknowledges that a significant portion of the services
performed by you on behalf of WII since January 1, 1998 was attributable to
pursuing WII's and its related and affiliated entities' interests outside of the
United States, including oversight of Arcadian, WII's United Kingdom-based
operating division, and that such services included oversight of operations,
acquisitions and strategy development for such foreign operations.

     12.  Arbitration of Disputes
          -----------------------

     Any controversy or claim arising out of or relating to this Agreement or
the breach thereof shall, to the fullest extent permitted by law, be settled by
arbitration in accordance with Paragraph 13 of the Employment Agreement. This
Section 12 shall be specifically enforceable. Notwithstanding the foregoing,
this Section 12 shall not preclude either party from pursuing a court action for
the sole purpose of obtaining a temporary restraining order or a preliminary
injunction in circumstances in which such relief is appropriate; provided that
                                                                 --------
any other relief shall be pursued through an arbitration proceeding pursuant to
this Section 12.
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 8


     13.  Consent to Jurisdiction
          -----------------------

     To the extent that any court action is permitted consistent with or to
enforce Section 12 of this Agreement, the parties hereby consent to the
jurisdiction of the state and federal courts in or for Dallas, Texas.
Accordingly, with respect to any such court action, you and the Companies (a)
submit to the personal jurisdiction of such courts; (b) consent to service of
process; and (c) waive any other requirement (whether imposed by statute, rule
of court, or otherwise) with respect to personal jurisdiction or service of
process.

     14.  Notices. Acknowledgments and Other Terms
          ----------------------------------------

          (a)  You are advised to consult with an attorney before signing this
Agreement.

          (b)  You acknowledge and agree that the Companies' promises in this
Agreement constitute consideration in addition to anything of value to which you
are otherwise entitled by reason of the termination of your employment.

          (c)  By signing this Agreement, you acknowledge that you are doing so
voluntarily and knowingly, fully intending to be bound by this Agreement. You
also acknowledge that you are not relying on any representations by any
representative of the Companies concerning the meaning of any aspect of this
Agreement. You understand that this Agreement shall not in any way be construed
as an admission by the Companies of any liability or any act of wrongdoing
whatsoever by the Companies against you and that the Companies specifically
disclaim any liability or wrongdoing whatsoever against you on the part of
themselves and their respective officers, directors, shareholders, employees and
agents.

          (d)  In the event of any dispute, this Agreement will be construed as
a whole, will be interpreted in accordance with its fair meaning, and will not
be construed strictly for or against either you or the Companies.

          (e)  The laws of the State of Texas will govern any dispute about this
Agreement, including any interpretation or enforcement of this Agreement.

          (f)  In the event that any provision or portion of a provision of this
Agreement shall be determined to be illegal, invalid or unenforceable, the
remainder of this Agreement shall be enforced to the fullest extent possible and
the illegal, invalid or unenforceable provision or portion of a provision will
be amended by a court of
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 9


competent jurisdiction to reflect the parties' intent if possible. If such
amendment is not possible, the illegal, invalid or unenforceable provision or
portion of a provision will be severed from the remainder of this Agreement and
the remainder of this Agreement shall be enforced to the fullest extent possible
as if such illegal, invalid or unenforceable provision or portion of a provision
was not included.

          (g)  This Agreement may be modified only by a written agreement signed
by you and authorized representatives of the Companies.

          (h)  This Agreement constitutes the entire agreement between the
parties with respect to the subject matter hereof and supersedes all prior
agreements between the parties with respect to any related subject matter;
provided, that the Indemnification Agreement shall remain in full force and
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effect in accordance with its terms.

          (i)  This Agreement shall be binding upon each of the parties and upon
their respective heirs, administrators, representatives, executors, successors
and assigns, and shall inure to the benefit of each party and to their heirs,
administrators, representatives, executors, successors, and assigns.

          (j)  This Agreement may be executed in one or more counterparts, all
of which taken together shall constitute one and the same Agreement.
<PAGE>

Mr. Karim Alibhai
July 7, 1999
Page 10

     If you agree to these terms, please sign and date below and return this
Agreement to the General Counsel of WII.

                                        Sincerely,


                                        WYNDHAM INTERNATIONAL, INC.



                                        By: /s/ JAMES D. CARREKER
                                           -------------------------------------
                                           James D. Carreker
                                           Chairman and Chief Executive Officer


                                        PATRIOT AMERICAN HOSPITALITY, INC.



                                        By: /s/ JAMES D. CARREKER
                                           -------------------------------------
                                           James D. Carreker
                                           Chief Executive Officer


Accepted and agreed to:

/s/ KARIM ALIBHAI
-----------------------                 ----------------------------------------
Karim Alibhai                           Date