<PAGE>   1
                                                                   EXHIBIT 10.35


                         GUARANTEE ASSUMPTION AGREEMENT



       GUARANTEE ASSUMPTION AGREEMENT dated as of February 26, 1999, by Iridium
(Potomac) LLC, a Delaware limited liability company (the "Additional Subsidiary
Guarantor"), in favor of THE CHASE MANHATTAN BANK, as administrative agent for
the lenders party to the Secured Credit Agreement referred to below (in such
capacity together with its successors in such capacity, the "Administrative
Agent").

       Iridium Operating LLC, a Delaware limited liability company, the lenders
named therein (the "Lenders"), the Global Lead Arrangers and Joint Book
Managers, the Administrative Agent and the Documentation Agent are parties to a
Senior Secured Credit Agreement dated as of December 23, 1998 (as modified,
supplemented or otherwise modified and in effect from time to time, the "Secured
Credit Agreement", the terms defined therein and not otherwise defined herein
being used as therein defined).

       Pursuant to Section 6.11 of the Secured Credit Agreement, the Additional
Subsidiary Guarantor hereby agrees to become a "Subsidiary Guarantor" for all
purposes of the Subsidiary Guarantee Agreement, and an "Obligor" for all
purposes of the Security Agreement. Without limiting the generality of the
foregoing, the Additional Subsidiary Guarantor hereby, jointly and severally
with the other Subsidiary Guarantors, guarantees to each Lender and each Agent
and their respective successors and assigns the prompt payment in full when due
(whether at stated maturity, by acceleration or otherwise) of all Guaranteed
Obligations (as defined in the Subsidiary Guarantee Agreement) in the same
manner and to the same extent as is provided in Article II of the Subsidiary
Guarantee Agreement. In addition, the Additional Subsidiary Guarantor hereby
makes the representations and warranties set forth in Article III of the
Subsidiary Guarantee Agreement, and in Article II of the Security Agreement,
with respect to itself and its obligations under this Agreement (with any
reference in said Sections to the Credit Documents being deemed to include a
reference to this Agreement). In addition, Annexes 1, 2, 3, 4, 5 and 6 to the
Security Agreement shall be deemed to be supplemented in respect of the
Additional Subsidiary Guarantor as specified in Appendix A hereto.


<PAGE>   2


       IN WITNESS WHEREOF, the Additional Subsidiary Guarantor has caused this
Guarantee Assumption Agreement to be duly executed and delivered as of the day
and year first above written.

                                     IRIDIUM (POTOMAC) LLC



                                     By   
                                          ------------------------------
                                          Roy Grant
                                          Vice President
                                          and Chief Financial Officer


Accepted and Agreed:

THE CHASE MANHATTAN BANK,
   as Administrative Agent



By   
     -------------------------
     Title:
<PAGE>   3


                                APPENDIX A TO THE GUARANTEE ASSUMPTION AGREEMENT
                                 Supplement to Annex 1 to the Security Agreement


                               PLEDGED COLLATERAL

                  [See Sections 2(b) and (c) and 3(a) and (b)]


<TABLE>
<CAPTION>
-----------------------------------------------------------------------------------
                                                   Type or Class of   Number of 
Issuer          Certificate Nos.   Registered      Ownership          Shares or 
                (if any)           Owner           Interests          Interests
-----------------------------------------------------------------------------------
<S>             <C>                <C>             <C>                <C>
Iridium         1                  Iridium         Interest           1
(Potomac) LLC                      Operating LLC                      
-----------------------------------------------------------------------------------
</TABLE>



<PAGE>   4


                                APPENDIX A TO THE GUARANTEE ASSUMPTION AGREEMENT
                                 Supplement to Annex 2 to the Security Agreement


                 LIST OF COPYRIGHTS, COPYRIGHT REGISTRATIONS AND
                    APPLICATIONS FOR COPYRIGHT REGISTRATIONS

                               [See Section 2(d)]

IRIDIUM (POTOMAC) LLC
---------------------
      None


<PAGE>   5


                                APPENDIX A TO THE GUARANTEE ASSUMPTION AGREEMENT
                                 Supplement to Annex 3 to the Security Agreement


                     LIST OF PATENTS AND PATENT APPLICATIONS

                               [See Section 2(d)]

IRIDIUM (POTOMAC) LLC
---------------------
     None


<PAGE>   6


                                APPENDIX A TO THE GUARANTEE ASSUMPTION AGREEMENT
                                 Supplement to Annex 4 to the Security Agreement


                LIST OF TRADE NAMES, TRADEMARKS, SERVICES MARKS,
                  TRADEMARK AND SERVICE MARK REGISTRATIONS AND
            APPLICATIONS FOR TRADEMARK AND SERVICE MARK REGISTRATIONS

                               [See Section 2(d)]

                                 U.S. TRADEMARKS

IRIDIUM (POTOMAC) LLC
---------------------
     None

                               FOREIGN TRADEMARKS

IRIDIUM (POTOMAC) LLC
---------------------
     None


<PAGE>   7


                                APPENDIX A TO THE GUARANTEE ASSUMPTION AGREEMENT
                                 Supplement to Annex 5 to the Security Agreement


                LIST OF CONTRACTS, LICENSES AND OTHER AGREEMENTS

                         [See Section 2(d), (e) and (f)]


IRIDIUM (POTOMAC) LLC
---------------------
     None



<PAGE>   8


                                APPENDIX A TO THE GUARANTEE ASSUMPTION AGREEMENT
                                 Supplement to Annex 6 to the Security Agreement


                                LIST OF LOCATIONS

                               [See Section 4.07]

IRIDIUM (POTOMAC) LLC
---------------------
Delaware - New Castle County
District of Columbia
Virginia - Loudoun County