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                                                                   Exhibit 3.126
                            CERTIFICATE OF AMENDMENT

                                     TO THE

                       CERTIFICATE OF LIMITED PARTNERSHIP

                                       OF

                 75 ARLINGTON HEIGHTS LIMITED PARTNERSHIP, L.P.

         The undersigned, desiring to amend the Certificate of Limited
Partnership of 75 Arlington Heights Limited Partnership, L.P. pursuant to the
provisions of Section 17-202 of the Revised Uniform Limited Partnership act of
the State of Delaware, does hereby certify as follows:

         FIRST. The name of the Limited Partnership is 75 Arlington Heights
Limited Partnership, L.P.

         SECOND: Article 3 of the Certificate of Limited Partnership shall be
amended as follows:

         MeriStar Hospitality Operating Partnership, L.P., whose office is
located at 1010 Wisconsin Avenue, NW, Washington, DC 20007, is the new general
partner of 75 Arlington Heights Limited Partnership, L.P.

         IN WITNESS WHEREOF, the undersigned executed this Amendment to the
Certificate of Limited Partnership on this Twenty-Sixth day of October, 1999.

                                  75 Arlington Heights Limited Partnership, L.P.

                                  By: /s/ Christopher L. Bennett
                                      -------------------------------------
                                          Christopher L. Bennett, VP Legal,
                                  MeriStar Hospitality Operating Partnership, LP
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                       CERTIFICATE OF LIMITED PARTNERSHIP

                                       OF

                 75 ARLINGTON HEIGHTS LIMITED PARTNERSHIP, L.P.

The undersigned, desiring to form a limited partnership under the laws of the
State of Delaware, does hereby certify as follows:

         1)       The name of the limited partnership is 75 Arlington Heights
                  Limited Partnership, L.P.

         2)       The address of the registered office of the limited
                  partnership is 1209 Orange Street, in the City of Wilmington,
                  in the County of New Castle, Delaware. The name of the limited
                  partnership's registered agent is The Corporation Trust
                  Company and its address is 1209 Orange Street, in the City of
                  Wilmington, in the County of New Castle, Delaware.

         3)       The name and mailing address of the Sole General Partner of
                  the limited partnership is:



                  Name                            Address
                  ----                            -------
                                               
                  AGH 75 Arlington Heights LLC    c/o American General Hospitality
                                                  Corporation
                                                  3860 W. Northwest Highway,
                                                  Suite 300
                                                  Dallas, TX 75220

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Dated: February 17th, 1997.

                              SOLE GENERAL PARTNER:

                              AGH 75 Arlington Heights LLC

                              By:   American General Hospitality Corporation,
                                    a member

                                    By:  /S/ KENNETH E. BARR
                                         -------------------------------
                                         Name:  Kenneth E. Barr
                                         Title: Executive Vice President

                              By:   American General Hospitality Operating
                                    Partnership, L.P., a member

                                    By:    AGH GP, Inc.,
                                           its general partner

                                      By:  /S/ KENNETH E. BARR
                                           -------------------------------
                                           Name:  Kenneth E. Barr
                                           Title: Executive Vice President