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                                                                   Exhibit 10.13

                      AMENDMENT TO NOTE PURCHASE AGREEMENT

          This Amendment (this "Amendment") to that certain Note Purchase
Agreement, dated as of December 21, 2002 (the "Agreement"), by and among XM
SATELLITE RADIO INC., a Delaware corporation (the "Company"), XM SATELLITE RADIO
HOLDINGS INC., a Delaware corporation and the sole stockholder of the Company
("Holdings" and, together with the Company, the "Obligors"), and OnStar
Corporation, a Delaware corporation ("OnStar" and, together with the Obligors,
the "Parties") is made as of January 16, 2003. Capitalized terms used herein but
not defined shall have the meanings ascribed to such terms in the Agreement.

                                    RECITALS

          WHEREAS, the Obligors have entered into an amendment (the "New Money
NPA Amendment") to the certain note purchase agreement, dated as of December 21,
2002, by and among the Obligors and the investors party thereto, pursuant to
which the Obligors have agreed to issue and sell, and certain investors have
agreed to purchase, up to an additional $25,000,000 in initial value of New
Notes; and

          WHEREAS, the Parties desire to enter into this Amendment to modify
certain definitions used in the Agreement and the other Transaction Documents to
give effect thereto.

                                    AGREEMENT

          NOW, THEREFORE, in consideration of the mutual promises and
representations contained herein and other good and valuable consideration, the
receipt and sufficiency of which are hereby expressly acknowledged, and
intending to be bound hereby, the Parties hereby agree as follows:

          1.   AMENDMENTS TO THE AGREEMENT.

          The following provisions of the Agreement shall be amended as set
forth below:

          (a)  Subsection (1) of the term "Concurrent Financing Transactions"
shall be amended for all purposes of the Agreement to mean the issuance of the
Obligors' 10% Senior Secured Discount Convertible Notes due 2009 to certain
investors in an initial aggregate principal amount of up to $210,000,000 (the
"New Notes").

          (b)  Appropriate revisions shall be made to each of the forms attached
as exhibits to the Agreement prior to execution in order to reflect the change
set forth in subsection (a) of this Section 1.

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          2.   MISCELLANEOUS

          (a)  The Parties agree to execute and deliver all such further
documents, agreements and instruments and take such other and further action as
may be necessary or appropriate to carry out the purposes and intent of this
Amendment.

          (b)  This Agreement may be executed in counterparts, which, when taken
together, shall constitute an original.

                               *   *   *   *   *

                                        2

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          IN WITNESS WHEREOF, the Parties have caused this Amendment to be duly
signed as of the date first above written.

OBLIGORS:

XM SATELLITE RADIO HOLDINGS INC.          XM SATELLITE RADIO INC.


By: /s/ Joseph M. Titlebaum               By: /s/ Joseph M. Titlebaum
   ------------------------------            -----------------------------------
Name: Joseph M. Titlebaum                 Name: Joseph M. Titlebaum
Title: Senior Vice President, General     Title: Senior Vice President, General
Counsel and Secretary                     Counsel and Secretary


ONSTAR CORPORATION

By:  /s/ Kenneth D. Enborg
   ------------------------------
Name:  Kenneth D. Enborg
Title: Vice President and General Counsel

                      Signature Page to Amendment to GM NPA