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                                                                     Exhibit 4.5

                       MERISTAR HOSPITALITY CORPORATION


                                      TO



                       IBJ SCHRODER BANK & TRUST COMPANY
                                    Trustee



                              SECOND SUPPLEMENTAL
                                   INDENTURE

                          Dated as of August 3, 1998
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                                                                               1

     SECOND SUPPLEMENTAL INDENTURE, dated as of August 3, 1998 between MeriStar
Hospitality Corporation, a Maryland corporation, having its principal office at
1010 Wisconsin Avenue, N.W., Suite 650, Washington, D.C. 20007 and IBJ Schroder
Bank & Trust Company, a banking corporation duly organized and existing under
the laws of the State of New York, as Trustee under the Indenture referred to
below (herein called the "Trustee").


                            RECITALS OF THE COMPANY

     WHEREAS, CapStar Hotel Company, a Delaware corporation ("CapStar") has
heretofore executed and delivered to the Trustee a certain indenture, dated as
of August 19, 1997 (the "Original Indenture"), as supplemented and amended by
the First Supplemental Indenture, dated as of March 20, 1998 (the "First
Supplement" and, together with the Original Indenture, the "Indenture"),
pursuant to which one series of senior subordinated notes of CapStar (herein
called the "Securities") were issued.  All terms used in this Second
Supplemental Indenture which are defined in the Indenture shall have the
meanings assigned to them in the Indenture;

     WHEREAS, CapStar and American General Hospitality Corporation, a Maryland
corporation ("AGH") have entered into an Agreement and Plan of Merger, dated as
of March 15, 1998 (the "Merger Agreement"), whereby CapStar will merge with and
into AGH (the "Merger"), with the result that AGH will be the surviving
corporation operating under the name MeriStar Hospitality Corporation (herein
called the "Company");

     WHEREAS, Section 5.1 of the Indenture provides that CapStar shall not enter
the Merger unless the Company assumes all the obligations of CapStar under the
Securities and the Indenture pursuant to a supplemental indenture;

     WHEREAS, Section 9.1 of the Indenture provides that without the written
consent of any Holder, the Company, when authorized by a resolution of its Board
of Directors, and the Trustee may enter into an indenture supplemental to the
Indenture to provide for the assumption of the Company's obligations to Holders
of the Securities under the Indenture in the case of a merger involving the
Company pursuant to Article 5 of the Indenture;

     WHEREAS, the Company pursuant to the foregoing authority, proposes in and
by this Second Supplemental Indenture to amend the Indenture upon the Merger
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                                                                               2

to reflect the assumption by the Company of all the obligations of CapStar under
the Securities and the Indenture; and

     WHEREAS, all things necessary to make this Second Supplemental Indenture a
valid agreement of the Company and the Trustee and a valid amendment of and
supplement to the Indenture have been done.
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                                                                               3

     NOW, THEREFORE, THIS SECOND SUPPLEMENTAL INDENTURE WITNESSETH:

     For and in consideration of the premises and the purchase of the Securities
by the Holders thereof, it is mutually covenanted and agreed, for the equal and
proportionate benefit of all Holders of the Securities as follows:


                                  ARTICLE ONE

                                 PROVISIONS OF
                              GENERAL APPLICATION

     SECTION 1.1  Assumption of Obligations.  The Company assumes all the
                  -------------------------
obligations of CapStar under the Securities and the Indenture.


                                  ARTICLE TWO

                                 MISCELLANEOUS

     SECTION 2.1  Incorporation of Indenture.  All the provisions of this
                  --------------------------
Second Supplemental Indenture shall be deemed to be incorporated in, and made a
part of, the Indenture; and the Indenture, as supplemented and amended by this
Second Supplemental Indenture, shall be read, taken and construed as one and the
same instrument.

     SECTION 2.2  Application of Second Supplemental Indenture.  The provisions
                  --------------------------------------------
and benefit of this Second Supplemental Indenture shall be effective with
respect to Securities outstanding prior to and after the execution hereof.

     SECTION 2.3  Headings.  The headings of the Articles and Sections of the
                  --------
Second Supplemental Indenture are inserted for convenience of reference and
shall not be deemed to be a part thereof.

     SECTION 2.4  Counterparts.  This Second Supplemental Indenture may be
                  ------------
executed in any number of counterparts, each of which so executed shall be
deemed to be an original, but all such counterparts shall together constitute
but one and the same instrument.

     SECTION 2.5  Conflict with Trust Indenture Act.  If any provision hereof
                  ---------------------------------
limits, qualifies or conflicts with another provision hereof which is required
to be included in this Second Supplemental Indenture by any of the provisions of
the Trust Indenture Act, such required provision shall control.
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          SECTION 2.6 Successors and Assigns.  All covenants and agreements in
                      ----------------------
this Second Supplemental Indenture by the Company shall bind its successors and
assigns, whether so expressed or not.

A.             SECTION 2.7    Separability Clause.  In case any provision in
                              -------------------
this Second Supplemental Indenture shall be invalid, illegal or unenforceable,
the validity, legality and enforceability of the remaining provisions shall not
in any way be affected or impaired thereby.

A.             SECTION 2.8    Governing Law.  The internal law of the State of
                              -------------
New York shall govern and be used to construe this Second Supplemental
Indenture.
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          IN WITNESS WHEREOF, the parties hereto have caused this Second
Supplemental Indenture to be duly executed, and their respective corporate seals
to be hereunto affixed and attested, all as of the day and year first above
written.
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                                                                               6


STATE OF            )
                    ) ss.:
COUNTY OF           )


          On the         day of                          , 1998, before me
personally came, to me known, who, being by me duly sworn, did depose and say
that he is of MERISTAR HOSPITALITY CORPORATION, one of the corporations
described in and which executed the foregoing instrument; that he knows the seal
of said corporation; that the seal affixed to said instrument is such corporate
seal; that it was so affixed by authority of the Board of Directors of said
corporation; and that he signed his name thereto by like authority.

                                             _______________________________

     Notary Public

[NOTARIAL SEAL]

My Commission Expires:


STATE OF            )
                    ) ss.:
COUNTY OF           )


          On the         day of                          , 1998, before me
personally came, to me known, who, being by me duly sworn, did depose and say
that he is of IBJ SCHRODER BANK & TRUST COMPANY, one of the corporations
described in and which executed the foregoing instrument; that he knows the seal
of said corporation; that the seal affixed to said instrument is such corporate
seal; that it was so affixed by authority of the Board of Directors of said
corporation; and that he signed his name thereto by like authority.

                                             _______________________________

     Notary Public

[NOTARIAL SEAL]

My Commission Expires: