UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 6-K

       REPORT OF FOREIGN PRIVATE ISSUER PURSUANT TO RULE 13a-16 or 15d-16
                   UNDER THE SECURITIES EXCHANGE ACT OF 1934

                          For the month of _June, 2004

                          GRUPO IUSACELL, S.A. de C.V.

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                 (Translation of registrant's name into English)

                                Montes Urales 460
                Col. Lomas de Chapultepec, Deleg. Miguel Hidalgo
                               11000, Mexico D.F.

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                     (Address of principal executive office)

Indicate by check mark whether the registrant files or will fill annual reports
under cover of Form 20-F or Form 40-F: Form 20-F __X__ Form 40-F ____

Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g-3-2(b) under the Securities and Exchange Act of
1934. Yes [ ] No [X]




Documents Furnished By the Registrant

1. Press Release of the Registrant dated June 1, 2004

                                   SIGNATURES

Pursuant to the requirements of the Securities and Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                            GRUPO IUSACELL, S.A. DE C.V.

Date: June 1, 2004                          /s/ Jose Luis Riera
                                            ----------------------------
                                            Name: Jose Luis Riera
                                            Title: Attorney in fact

                                            /s/ Fernando Cabrera
                                            ----------------------------
                                            Name: Fernando Cabrera
                                            Title: Attorney in fact



[LOGO] Iusacell                                                INVESTOR CONTACTS

                                                              Jose Luis Riera K.
                                                         Chief Financial Officer
                                                                  5255-5109-5927

                                                                J. Victor Ferrer
                                                                 Finance Manager
                                                                  5255-5109-5927
                                                         vferrer@iusacell.com.mx

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Iusacell Anounces
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Mexico City, June 1, 2004 - Grupo Iusacell, S.A. de C.V. [BMV: CEL, NYSE: CEL]
announced today that did not make the US$24.9 million interest payment
corresponding to the 14.25% bond of US$350 million due in 2006.

On the other hand and regarding the press release dated May 28, in which the
Company informed about the nonpayment of the first amortization of the principal
of the Amended and Restated Senior Secured Loan Agreement of US$266 million, the
Company wants to clarify that it referred to the Credit Agreement dated March
29, 2001(Syndicated Loan) executed by its main subsidiary, Grupo Iusacell
Celular, S.A. de C.V. (Grupo Iusacell Celular).

The company continues to work in it debt restructuring process and the debt
restructure of Grupo Iusacell Celular and subsidiaries.

                             **********************

About Iusacell
--------------

Grupo Iusacell, S.A. de C.V. (Iusacell, NYSE: CEL; BMV: CEL) is a wireless
cellular and PCS service provider in seven of Mexico's nine regions, including
Mexico City, Guadalajara, Monterrey, Tijuana, Acapulco, Puebla, Leon and Merida.
The Company's service regions encompass a total of approximately 92 million
POPs, representing approximately 90% of the country's total population.

Grupo Iusacell, S.A. de C.V. press releases and all other written materials may
from time to time contain statements about expected future events and financial
results that are forward-looking and subject to risks and uncertainties. For
those statements, the Company claims the protection of the safe harbor for
forward-looking statements contained in the Private Securities Litigation Reform
Act of 1995. Discussion of factors that may affect future results is contained
in our filings with the Securities and Exchange Commission.