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                                                                   Exhibit 10.32


                          SECOND SUPPLEMENTAL INDENTURE

                  This SECOND SUPPLEMENTAL INDENTURE (this "Supplemental
Indenture"), dated as of January 14, 1999, among Radio Unica Corp., a Delaware
corporation (the "Company"), Radio Unica of New York, Inc., a Delaware
corporation ("RUNY"), Radio Unica of New York License Corp., a Delaware
corporation ("RUNY License"), Radio Unica of Dallas, Inc., a Delaware
corporation ("RUD"), Radio Unica of Dallas License Corp., a Delaware corporation
("RUD License"), Radio Unica of Phoenix, Inc., a Delaware corporation ("RUP"),
Radio Unica of Phoenix License Corp., a Delaware corporation ("RUP License") and
Wilmington Trust Company, a Delaware banking corporation, as trustee (the
"Trustee"). RUNY, RUNY License, RUD, RUD License, RUP and RUP License are each,
directly or indirectly, wholly owned subsidiaries of the Company and are
collectively referred to herein as the Additional Guarantors.

WITNESSETH

                  WHEREAS, the Company, the guarantors named therein and the
Trustee have heretofore executed an indenture (the "Indenture"), dated as of
July 27, 1998, providing for the issuance of an aggregate principal amount at
maturity of $158,088,000 of the Company's 11 3/4% Senior Discount Notes due 2006
(the "Notes");

                  WHEREAS, the Company, the additional guarantors named therein
and the Trustee have heretofore executed a First Supplemental Indenture, dated
as of September 11, 1998, in connection with the closing of the transactions
contemplated by the Stock Purchase Agreement, dated as of June 10, 1998, among
the Company, Joaquin F. Blaya, and Blaya, Inc.;

                  WHEREAS, each of the Additional Guarantors became a Restricted
Subsidiary (as defined in the Indenture) of the Company as of January 14, 1999;

                  WHEREAS, Section 10.03 of the Indenture requires that the
Company cause any Person (as defined in the Indenture) which becomes a
Restricted Subsidiary (other than a Foreign Restricted Subsidiary (as defined in
the Indenture)) to execute a supplemental indenture pursuant to which such
Restricted Subsidiary shall guarantee the obligations of the Company under the
Notes and the Indenture; and

                  WHEREAS, pursuant to Sections 8.01 and 10.03 of the Indenture,
the Trustee is authorized to execute and deliver this Supplemental Indenture and
Section 8.01 of the Indenture provides that the Company may amend the Indenture
without notice to or consent of any Noteholder to add a Guarantor;

                  NOW THEREFORE, in consideration of the foregoing and for other
good and valuable consideration, the receipt of which is hereby acknowledged,
the


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Company, the Additional Guarantors and the Trustee mutually covenant and agree
for the equal and ratable benefit of the holders of the Notes as follows:

         1. DEFINITIONS. (a) Capitalized terms used herein without definition
shall have the meaning assigned to them in the Indenture.

                         (b) For all purposes of this Supplemental Indenture, 
except as otherwise herein expressly provided or unless the context otherwise
requires: (i) the terms and expressions used herein shall have the same meanings
as corresponding terms and expressions used in the Indenture; and (ii) the words
"herein," "hereof" and "hereby" and other words of similar import used in this
Supplemental Indenture refer to this Supplemental Indenture as a whole and not
to any particular section hereof.

         2. AGREEMENT TO GUARANTEE. Each of the Additional Guarantors hereby
agrees, jointly and severally with all other Guarantors under the Indenture, to
guarantee the obligations of the Company under the Notes and the Indenture in
accordance with Article 10 of the Indenture with the same effect and to the same
extent as if each Additional Guarantor had been named in the Indenture as a
Guarantor. Except as expressly amended hereby, the Indenture is in all respects
ratified and confirmed and all the terms, conditions and provisions thereof
shall remain in full force and effect. This Supplemental Indenture shall form a
part of the Indenture for all purposes, and every holder of Notes heretofore or
hereafter authenticated and delivered shall be bound hereby.

         3. GOVERNING LAW. This Supplemental Indenture 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 conflict of laws. The Additional Guarantors agree 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 Supplemental Indenture.

         4. TRUSTEE MAKES NO REPRESENTATION. The Trustee makes no representation
as to the validity or sufficiency of this Supplemental Indenture.

         5. COUNTERPARTS. The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of them
together represent the same agreement.

         6. EFFECT OF HEADINGS. The Section headings herein are for convenience
only and shall not effect the construction thereof.

                  IN WITNESS WHEREOF, the parties hereto have caused this
Supplemental Indenture to be duly executed as of the date first above written.

RADIO UNICA CORP.



By:
   ------------------------------------------
Name: Joaquin F. Blaya
Title: Chairman and Chief Executive Officer



RADIO UNICA OF NEW YORK, INC.



By:
   ------------------------------------------
Name:  Joaquin F. Blaya
Title:  Chairman and Chief Executive Officer


RADIO UNICA OF NEW YORK LICENSE CORP.



By:
   ------------------------------------------
Name:  Joaquin F. Blaya
Title:  Chairman and Chief Executive Officer


RADIO UNICA OF DALLAS, INC.



By:
   ------------------------------------------
Name:  Joaquin F. Blaya
Title:  Chairman and Chief Executive Officer


RADIO UNICA OF DALLAS LICENSE CORP.



By:
   ------------------------------------------
Name:  Joaquin F. Blaya
Title:  Chairman and Chief Executive Officer


RADIO UNICA OF PHOENIX, INC.



By:
   ------------------------------------------
Name:  Joaquin F. Blaya
Title:  Chairman and Chief Executive Officer


RADIO UNICA OF PHOENIX LICENSE CORP.


By:
   ------------------------------------------
Name:  Joaquin F. Blaya
Title:  Chairman and Chief Executive Officer


WILMINGTON TRUST COMPANY, as
Trustee



By:
   ------------------------------------------
Name: Bruce L. Bisson
Title: Vice President