MERISTAR HOSPITALITY CORPORATION NON-EMPLOYEE DIRECTORS INCENTIVE PLAN ARTICLE I

Exhibit 10.5.2

MERISTAR HOSPITALITY CORPORATION

NON-EMPLOYEE DIRECTORS’ INCENTIVE PLAN

ARTICLE I

Definitions

1.1 Award Date means the first business day following the Company’s annual meeting of stockholders, beginning with the annual meeting of stockholders in 1999.

1.2 Board means the Board of Directors of the Company.

1.3 Committee means the Board or the committee appointed by the Board to administer the Plan.

1.4 Common Stock means the common stock of the Company.

1.5 Company means MeriStar Hospitality Corporation, a Maryland corporation.

1.6 Fair Market Value means, on any given date: if the Common Stock is not listed on an established stock exchange, Fair Market Value shall be the average of the final bid and asked quotations on the over-the-counter market in which the Common Stock is traded or, if applicable, the reported “closing” price of a share of Common Stock in the New York over-the-counter market as reported by the National Association of Securities Dealers, Inc. If the Common Stock is listed on one or more established stock exchanges, Fair Market Value shall be deemed to be the highest closing price of a share of Common Stock reported on any of such exchanges. In any case, if no sale of Common Stock is made on any stock exchange or over-the-counter market on that date, then Fair Market Value shall be determined as of the next preceding day on which there was a sale.

1.7 First Award Date means the date following the consummation of the merger contemplated by the Agreement and Plan of Merger among American General Hospitality Corporation and American General Hospitality Operating Partnership, L.P., and Capstar Hotel Company, Capstar Management Company, L.P. and Capstar Management Company II, L.P., dated as of March 15, 1998, upon which the Participant commences service as a member of the Board, whether by election or appointment.

1.8 Internal Revenue Code means the Internal Revenue Code of 1986, as amended.

1.9 Option means a stock option that entitles the holder to purchase shares of Common Stock from the Company on the terms set forth in Article IV of this Plan.

1.10 Participant means a member of the Board who, on the First Award Date or applicable Award Date, is not an employee or officer of the Company or any “subsidiary” or “parent” corporation of the Company within the meaning of Section 424 of the Internal Revenue Code.

1.11 Plan means the MeriStar Hospitality Corporation Non-Employee Directors’ Incentive Plan.

ARTICLE II

Purposes

The Plan is intended to (i) assist the Company in recruiting and retaining non-employee directors and (ii) promote a greater identity of interest between Participants and stockholders by enabling Participants to participate in the Company’s future success.

ARTICLE III

Administration

The Plan shall be administered by the Committee. The Committee shall have complete authority to interpret all provisions of the Plan; to adopt, amend, and rescind rules and regulations pertaining to the administration of the Plan and to make all other determinations necessary or advisable for the administration of the Plan. The express grant in the Plan of any specific power to the Committee shall not be construed as limiting any power or authority of the Committee. Any decision made, or action taken, by the Committee in connection with the administration of the Plan shall be final and conclusive. No member of the Committee shall be liable for any act done in good faith with respect to the Plan. All expenses of administering the Plan shall be borne by the Company.

ARTICLE IV

Options & Common Stock Grants

4.1 Grant of Options. Each Participant shall be granted an Option for 7,500 shares of Common Stock on the applicable First Award Date. Thereafter, each Participant shall receive an annual grant of Common Stock on each Award Date having a Fair Market Value of $20,000. All Options shall be evidenced by Agreements that shall be subject to the applicable provisions of this Plan and to such other provisions as the Committee may adopt which are not inconsistent with the provisions of this Plan.

4.2 Option Price. The price per share of Common Stock purchased on the exercise of an Option shall be the Fair Market Value on the date that the Option is granted.

4.3 Maximum Option Period. The maximum period during which an Option may be exercised shall be ten years from the date of grant.

4.4 Exercise of Options. All Options granted under the Plan shall vest in three annual installments beginning on the date of grant and on subsequent anniversaries thereof (each, a “Vesting Date”), provided the Participant continues to serve as a director of the Company on such Vesting Date.

4.5 Effect of Termination of Services or Death. If a Participant ceases to serve as a director of the Company for any reason, the Options that have been previously granted to that Participant and that are not vested as of that date shall be forfeited. Options that have vested as of the date of such cessation of services may be exercised by the Participant, in accordance with and subject to the terms of the Plan, after the date such Participant ceases to be a director of the Company. If a Participant dies, the Options that have been previously granted to that Participant and that are vested as of the date of death may be exercised by the administrator of the Participant’s estate, or by the person to whom such Options are transferred by will or the laws of descent and distribution. In no event, however, may any Option be exercised after the expiration date of such Option. Any Option or portion thereof that is not exercised during the applicable time period specified above shall be deemed terminated at the end of the applicable time period for purposes of Article VI hereof.

4.6 Effect of a Change in Control. All Options granted pursuant to this Plan shall immediately vest upon a Change in Control of the Company. For purposes of the Plan, a “Change in Control” shall mean (i) the commencement of a public tender offer for all or any portion of the Common Stock, (ii) a proposal to merge, consolidate or otherwise combine with another company is submitted to the stockholders of the Company for approval, or (iii) the Board approves any transaction or event that would constitute a change of control of the Company of a nature that would be required to be reported in response to Item 6(e) of Schedule 14A of the Securities Exchange Act of 1934, as amended.

4.7 Payment of Option Price. Payment of the Option price shall be made in cash, cash equivalent acceptable to the Committee, Company Common Stock, or a combination thereof. In addition, a Participant may provide instructions to the Company that upon receipt of the Option price in cash from a broker or dealer acting at the direction of the Participant in payment for any shares of Common Stock pursuant to the exercise of an Option, the Company shall issue such shares of Common Stock directly to the designated broker or dealer. If shares of Common Stock are surrendered in payment of the Option price, the shares

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surrendered must have an aggregate Fair Market Value (determined as of the day preceding the exercise date) that, together with any cash or cash equivalent paid, is not less than the Option price for the number of shares of Common Stock for which this Option is being exercised.

4.8 Nontransferability. Each Option granted under this Plan shall be nontransferable except by will or by the laws of descent and distribution. During the lifetime of the Participant to whom an Option is granted, the Option may be exercised only by the Participant. No right or interest of a Participant in any Option shall be liable for, or subject to, any lien, obligation, or liability of such Participant.

4.9 Transferable Options. Section 4.8 hereof to the contrary notwithstanding, an Option may be transferred by a Participant to the Participant’s children, grandchildren, spouse, one or more trusts for the benefit of such family members or a partnership in which such family members are the only partners; provided, however, that the Participant may not receive any consideration for the transfer. The holder of an Option transferred pursuant to this section shall be bound by the same terms and conditions that governed the Option during the period that it was held by the Participant.

4.10 Stockholder Rights. No Participant shall have any rights as a stockholder with respect to shares of Common Stock subject to his or her Option until the date of exercise of such option.

ARTICLE V

Shares in Lieu of Fees

5.1 Each Participant shall have the right to elect to receive payment of any or all director fees in shares of Common Stock rather than cash. Unless a Participant elects otherwise, fees paid in shares of Common Stock will be paid at the same time as are fees paid in cash.

ARTICLE VI

Stock Subject to Plan

6.1 Shares Issued. Upon the exercise of an Option, the Company may deliver to the Participant (or the Participant’s broker if the Participant so directs), shares of Common Stock from its authorized but unissued Common Stock.

6.2 Aggregate Limit. The maximum aggregate number of shares of Common Stock that may be issued under this Plan is the total of (i) two percent (2%) of the number of shares of Common Stock that were outstanding as of the end of the immediately preceding calendar year (rounded downward if necessary to eliminate fractional shares); minus (ii) the number of shares subject to awards granted under the Plan through the last day of the immediately preceding calendar year; plus (iii) as of the last day of the immediately preceding calendar year, the number of shares with respect to which previously granted awards under the Plan have expired or have been forfeited. The maximum aggregate number of shares that may be issued under this Plan shall be subject to adjustment as provided in Article VII.

6.3 Reallocation of Shares. If an Option is terminated, in whole or in part, for any reason other than its exercise, the number of shares of Common Stock allocated to the Option or portion thereof may be reallocated to other Options to be granted under this Plan.

ARTICLE VII

Adjustment Upon Change in Common Stock

The provisions of this Plan and the terms of outstanding Options shall be adjusted as the Committee shall determine to be equitably required in the event that there is an increase or reduction in the number of shares of Common Stock, or any change (including, but not limited to, a change in value) in the shares of Common Stock or exchange of shares of Common Stock for a different number or kind of shares or other securities of the Company by reason of a reclassification, recapitalization, merger, consolidation, reorganization, spin-off, split-up, subdivision or consolidation of shares, extraordinary dividend, change in

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corporate structure or otherwise. Any determination made under this Article VII by the Committee shall be final and conclusive.

The issuance by the Company of shares of any class, or securities convertible into shares of any class, for cash or property, or for labor or services, either upon direct sale or upon the exercise of rights or warrants to subscribe therefor, or upon conversion of shares of obligations of the Company convertible into such shares or other securities, shall not affect, and no adjustment by reason thereof shall be made with respect to, the provisions of this Plan or the terms of outstanding Options.

ARTICLE VIII

Compliance With Law and

Approval of Regulatory Bodies; Governing Law

No Common Stock shall be issued and no certificates for shares of Common Stock shall be delivered under the Plan except in compliance with all applicable federal and state laws and regulations, any listing agreement to which the Company is a party, and the rules of all domestic stock exchanges on which the Company’s Common Stock may be listed. The Company shall have the right to rely on an opinion of its counsel as to such compliance. Any certificate issued to evidence Common Stock issued upon the exercise of an Option granted under the Plan may bear such legends and statements as the Committee may deem advisable to assure compliance with federal and state laws and regulations. No Common Stock shall be issued and no certificate for shares of Common Stock shall be delivered upon the exercise of an Option granted under the Plan until the Company has obtained such consent or approval as the Committee may deem advisable from regulatory bodies having jurisdiction over such matters. Except as to matters of federal law, this Plan and the rights of all persons claiming hereunder shall be construed and determined in accordance with the laws of the State of Maryland without giving effect to conflicts of law principles.

ARTICLE IX

General Provisions

9.1 Unfunded Plan. The Plan, insofar as it provides for awards, shall be unfunded, and the Company shall not be required to segregate any assets that may at any time be represented by awards under the Plan. Any liability of the Company to any person with respect to any award to be made under the Plan shall be based solely upon any contractual obligations that may be created pursuant to the Plan. No such obligation of the Company shall be deemed to be secured by any pledge of, or other encumbrance on, any property of the Company.

9.2 Rules of Construction. Headings are given to the articles and sections of the Plan solely as a convenience to facilitate reference. The reference to any statute, regulation, or other provision of law shall be construed to refer to any amendment to or successor of such provision of law.

ARTICLE X

Amendment

The Board may amend from time to time or terminate the Plan at any time; provided, however, that no amendment may become effective until stockholder approval is obtained if the amendment (i) materially increases the aggregate number of shares of Common Stock that may be issued under this Plan or (ii) stockholder approval would be required for compliance with stock exchange rules. No amendment shall, without a Participant’s consent, adversely affect any rights of such Participant under any outstanding Option.

ARTICLE XI

Duration of Plan

No Option may be made under this Plan after December 31, 2008. Options made before that date shall remain valid in accordance with their terms.

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ARTICLE XII

Effective Date of Plan

The Plan was originally adopted by the Board on July 11, 1996 and approved by shareholders on July 15, 1996. The Plan was subsequently amended by the Board on April 3, 1998, which amendments were approved by the stockholders on July 28, 1998.

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