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 _May, 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 May 28, 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: May 28, 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

Mexico City, May 28, 2004 - Grupo  Iusacell,  S.A. de C.V. [BMV: CEL, NYSE: CEL]
announced that its principal  subsidiary,  Grupo Iusacell Celular, S.A. de C.V.,
did not make the US$33.2 million payment corresponding to the first amortization
of principal of the Amended and Restated Credit of US$266 million.

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

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.