<PAGE>   1
                                                                  EXHIBIT 10.34b



                                WAIVER UNDER THE
                              TERM CREDIT AGREEMENT

     WAIVER dated as of May 21, 1999 under the $100,000,000 Term Credit
Agreement dated as of March 31, 1998 (as heretofore amended, the "TERM CREDIT
AGREEMENT") among AMERICAN MOBILE SATELLITE CORPORATION (the "BORROWER"), the
BANKS party thereto (the "BANKS"), MORGAN GUARANTY TRUST COMPANY OF NEW YORK, as
Documentation Agent (the "DOCUMENTATION AGENT"), and TORONTO DOMINION (TEXAS),
INC., as Administrative Agent (the "ADMINISTRATIVE AGENT").


                             W I T N E S S E T H :

     WHEREAS, in exchange for up to 8,620,000 shares of the Borrower's common
stock, the Borrower desires to acquire 25 shares of common stock of AMRC
Holdings and certain other securities issued by AMRC Holdings from a trust (the
"TRUST") for the benefit of the shareholders of WorldSpace, Inc. (the
"EXCHANGE");

     WHEREAS, promptly after the Exchange, each share of Common Stock of AMRC
Holdings held by the Borrower will be exchanged for one share of Class B Common
Stock of AMRC Holdings;

     WHEREAS, the undersigned Banks and the Shareholder Guarantors are willing
to consent to the foregoing and to waive certain provisions of the Term Credit
Agreement in connection with the foregoing;

     NOW, THEREFORE, the undersigned parties hereto agree as follows:

     Section 1.  Definitions; References. Unless otherwise specifically defined
herein, each term used herein which is defined in the Term Credit Agreement has
the meaning assigned to such term in the Term Credit Agreement.

     Section 2.  Waiver. The undersigned Banks hereby waive the failure by the
Borrower to comply with Section 5.13 of the Term Credit Agreement in connection
with the Exchange.

     Section 3.  Exchange of Common Stock. The undersigned Banks and Shareholder
Guarantors (including Hughes in its capacity as agent for the Shareholder
Guarantors) hereby instruct the Collateral Agent to release the shares of Common
Stock of AMRC Holdings held by it pursuant to the Security and Pledge Agreement


<PAGE>   2
and the Shareholder Guarantor Security Agreement upon receipt of an equal number
of shares of Class B Common Stock of AMRC Holdings, together with stock powers
executed in blank.

     Section 4.  Representations of Borrower. The Borrower represents and
warrants that (i) the representations and warranties set forth in Article 4 of
the Term Credit Agreement shall be true on and as of the Effective Date and
(ii) no Default shall have occurred and be continuing on such date.

     Section 5.  Governing Law. This Waiver shall be governed by and construed
in accordance with the laws of the State of New York.

     Section 6.  Counterparts. This Waiver may be signed in any number of
counterparts, each of which shall be an original, with the same effect as if the
signatures thereto and hereto were upon the same instrument.

     Section 7.  Effectiveness. This Waiver shall become effective as of the
date hereof on the date (the "EFFECTIVE DATE") when the Documentation Agent
shall have received a counterpart hereof from each of the Borrower, Hughes,
SingTel, Baron Capital and the Required Banks signed by such party or a
facsimile or other written confirmation (in form satisfactory to the
Documentation Agent) that such party has signed a counterpart hereof.

     Section 8.  Shareholder Guarantor Consent. The Shareholder Guarantors
consent to the foregoing.

                                       2



<PAGE>   3
     IN WITNESS WHEREOF, the parties hereto have caused this Waiver to be duly
executed as of the date first above written.




                                             AMERICAN MOBILE SATELLITE
                                              CORPORATION


                                             By     /s/ Richard J. Burnheimer
                                             -----------------------------------
                                             Title: V.P. and Treasurer




                                             TORONTO DOMINION (TEXAS), INC., as
                                              Administrative Agent and Bank


                                             By     /s/ Jano Mott
                                             -----------------------------------
                                             Title: Vice President




                                             MORGAN GUARANTY TRUST
                                              COMPANY OF NEW YORK


                                             By     /s/ Robert Bottamed
                                             -----------------------------------
                                             Title: Vice President




                                             BANK OF AMERICA NATIONAL TRUST
                                              AND SAVINGS ASSOCIATION


                                             By     /s/ Diane P. Allen
                                             -----------------------------------
                                             Title: Vice President


<PAGE>   4
                                             BANCA COMMERCIALE ITALIANA LOS
                                              ANGELES FOREIGN BRANCH


                                             By     /s/ J. Wityak
                                             ---------------------------------
                                             Title: Vice President




                                             BANCA DI ROMA-SAN FRANCISCO


                                             By
                                             ---------------------------------
                                             Title:


                                             By
                                             ---------------------------------
                                             Title:




                                             THE CHASE MANHATTAN BANK


                                             By
                                             ---------------------------------
                                             Title:




                                             CITIBANK, N.A.


                                             By
                                             ---------------------------------
                                             Title:





<PAGE>   5
                                             DEUTSCHE BANK AG, NEW YORK
                                              BRANCH AND/OR CAYMAN ISLANDS
                                              BRANCH


                                             By     /s/ Joel Makowsky
                                             -----------------------------------
                                             Title: Vice President


                                             By     /s/ Virginia Mahler Cosenza
                                             -----------------------------------
                                             Title: Assistant Vice President




                                             THE FIRST NATIONAL BANK OF
                                              CHICAGO


                                             By     /s/ Kandis A. Jaffrey
                                             -----------------------------------
                                             Title: Assistant Vice President




                                             ISTITUTO BANCARIO SAN PAOLO DI
                                              TORINO ISTITUTO MOBILIARE
                                              ITALIANO S.P.A.


                                             By
                                             -----------------------------------
                                             Title:


                                             By
                                             -----------------------------------
                                             Title:




                                             NATIONSBANK, N.A.


                                             By     /s/ Diane P. Allen
                                             -----------------------------------
                                             Title: Vice President

<PAGE>   6
                                             HUGHES ELECTRONICS CORPORATION,
                                              as Guarantor and agent for the
                                              Shareholder Guarantors


                                             By     /s/ Mark A. McEachen
                                             -----------------------------------
                                             Title: Corporate V.P. and Treasurer




                                             SINGAPORE TELECOMMUNICATIONS
                                              LTD.


                                             By     /s/ Hoh Wing Chee
                                             -----------------------------------
                                             Title: V.P. (International Network)




                                             BARON CAPITAL PARTNERS, L.P., a
                                              Delaware limited partnership
                                             By: BARON CAPITAL MANAGEMENT,
                                              INC., a general partner


                                             By     /s/ Morty Schaja
                                             -----------------------------------
                                             Title: Senior Vice President and
                                                    Chief Operating Officer