<PAGE>
                                                                   EXHIBIT 10.68

                               GUARANTY AGREEMENT

      THIS GUARANTY AGREEMENT (this "GUARANTY") is made and delivered as of this
31s day of December, 2002, by SPANISH BROADCASTING SYSTEM, INC., a Delaware
corporation ("GUARANTOR") in favor of BIG CITY RADIO, INC., a Delaware
corporation ("BCR") and BIG CITY RADIO-CHI, L.L.C., a Delaware limited liability
company ("BCR-CHI"; BCR together with BCR-CHI, "SELLER").

      WHEREAS, Seller has entered into an Asset Purchase Agreement, dated as of
even date herewith (the "ASSET PURCHASE AGREEMENT") with Spanish Broadcasting
System of Illinois, Inc., a Delaware corporation ("PURCHASER");

      WHEREAS, BCR-CHI has entered into a Time Brokerage Agreement, dated as of
even date herewith (the "TIME BROKERAGE AGREEMENT") with Purchaser, which shall
become effective as of January 6, 2003; and

      WHEREAS, Guarantor is the parent corporation of Purchaser and desires that
Seller execute the Asset Purchase Agreement and that BCR-CHI execute the Time
Brokerage Agreement.

      NOW, THEREFORE, for value received, Guarantor hereby agrees as follows:

      1. Guarantor irrevocably and unconditionally guarantees to Seller the
prompt performance and payment when due of all of Purchaser's obligations under
the Asset Purchase Agreement and the Time Brokerage Agreement (the
"OBLIGATIONS"), including but not limited to the payment of the purchase price
and fee thereunder.

      2. The obligations of Guarantor under this Guaranty shall be absolute,
unconditional and irrevocable, and shall remain in full force and effect until
the Obligations shall have been satisfied in full, it being the express purpose
and intent of Guarantor that its obligations hereunder shall not be discharged
except by payment, performance, discharge or other satisfaction in full of all
of Guarantor's obligations hereunder. Such obligations shall not be in any
manner whatsoever affected, modified or impaired by the happening from time to
time of any assignment of Purchaser's Obligations to a third party or any event
or action that would, in the absence of this clause, result in the release or
discharge of Guarantor, by operation of law or otherwise, from the performance
of observance of any obligation, covenant or agreement contained in this
Guaranty, or the default
<PAGE>
or failure of Guarantor to perform fully any obligations set forth in this
Guaranty.

      3. Guarantor waives diligence, presentment, protest, notice, demand,
dishonor and notice of dishonor and any other defenses available to it hereunder
as a surety and agrees to be bound to the Obligations as fully as if it were a
co-obligor. The parties to the Asset Purchase Agreement and the Time Brokerage
Agreement may enter into any amendment, waiver or modification of the Asset
Purchase Agreement or the Time Brokerage Agreement, as the case may be, whether
or not such amendment, waiver or modification would in any way increase or
decrease the extent of Guarantor's obligations hereunder, without notice to or
consent of Guarantor and without thereby releasing Guarantor hereunder or
incurring any liability to Guarantor.

      4. No failure or delay or lack of demand, notice or diligence in
exercising any right under this Guaranty shall operate as a waiver thereof, nor
shall any single or partial exercise of any such right preclude any other or
further exercise thereof or the exercise of any other right under this Guaranty.

      5. This Guaranty is an absolute, unconditional and continuing guaranty of
payment and performance and not of collection. Seller need not exhaust or pursue
any remedy or take any action in respect of the default of any obligation
guaranteed hereby prior to or as a condition to proceeding directly under this
Guaranty against Guarantor.

      6. Guarantor represents and warrants to Seller that it has the corporate
power and authority to enter into this Guaranty, that all corporate and
governmental approvals needed by it to enter into and to perform this Guaranty
have been secured or obtained, and that this Guaranty is a legal and valid
obligation binding upon it and is enforceable in accordance with its terms, and
that the execution of this Guaranty does not conflict with any agreement,
undertaking, or instrument to which it is party. The undersigned represents that
he or she is fully authorized to execute and deliver this Guaranty on behalf of
Guarantor.

      7. Guarantor agrees that the obligation of Guarantor as a guarantor shall
not be impaired, modified, changed, released, or limited in any manner
whatsoever by any impairment, modification, change, release, or ]imitation of
the liability of Purchaser or its estate in bankruptcy, resulting from the
operation of any present or future provision of the bankruptcy laws or other
similar statute, or from the decision of any court.


                                        2
<PAGE>
      8. Guarantor agrees that its obligations hereunder are irrevocable, are
joint and several, and are independent of the obligations of Purchaser; that a
separate action or actions may be brought and prosecuted against Guarantor
regardless of whether any action is brought against Purchaser or whether
Purchaser is joined in any such action or actions; and that Guarantor waives the
benefit of any statute of limitations affecting its liability hereunder or the
enforcement hereof.

      9. Guarantor agrees to pay all costs, expenses and fees which may be
incurred by Seller in enforcing this Guaranty or in protecting the rights of
Seller following any default on the part of Guarantor hereunder, whether the
same shall be enforced by suit or otherwise.

      10. This Guaranty is and shall be in every particular available to the
successors and assigns of Seller and is and shall always be fully binding upon
the successors and assigns of Guarantor, provided that Guarantor shall not
assign any of its rights or obligations hereunder without the written consent of
Seller.

      11. This Guaranty shall be governed by and construed in accordance with
the laws of the State of New York as applied to contracts made and performed
within the State of New York, without regard to principles of conflicts of law.
Each of the parties hereto agrees to submit to the jurisdiction of the courts of
the State of New York in any action or proceeding arising out of or relating to
this Guaranty.


                                        3
<PAGE>
                  Executed as of the date first written above.

                                                  SPANISH BROADCASTING
                                                  SYSTEM, INC.


                                                   By: /s/ RAUL ALARCON, JR.
                                                      -------------------------

Accepted:

BIG CITY RADIO, INC.

By: /s/ DAVID A. PERSING
    ------------------------


BIG CITY RADIO-CHI, L.L.C.

By: /s/ DAVID A. PERSING
    ------------------------



                                        4