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 _April, 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 April 20, 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: April 2004, 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
       Pensamos en ti

                                                               INVESTOR CONTACTS

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

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

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Iusacell Announces
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Mexico City,  April 20, 2004 - Grupo  Iusacell,  S.A. de C.V.,  [BMV: CEL, NYSE:
CEL],  announced  today, in connection with the lawsuit filed on January 2004 by
certain  holders of the Senior Notes due 2004 against its principal  subsidiary,
Grupo Iusacell Celular,  S.A. de C.V. ("Iusacell Celular") and others,  alleging
breach of the Senior Note Indenture,  that Iusacell Celular moved to dismiss the
portion of the complaint  that requested that the Court declare that the holders
are  entitled to the benefit of liens senior to or at least equal in priority to
liens held by other creditors.

In response to the motion to dismiss, the holders filed an amended complaint and
are now also  are  seeking  injunctive  relief  barring  Iusacell  Celular  from
selling,  transferring or otherwise  encumbering the assets pending  decision on
the merits of their claim for specific performance. The time in which to respond
to the amended  complaint and the request for an injunction has not yet expired.
Iusacell  Celular  will  respond  to  the  amended  complaint  and  request  for
injunctive relief in due course.

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

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.