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 July, 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 July 7, 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: July 12, 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 Offier
                                                                  5255-5109-5927

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

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         The Supreme Court, New York County denies request vs. Iusacell

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Mexico City, July 7, 2004 - Grupo  Iusacell,  S.A. de C.V. [BMV: CEL, NYSE: CEL]
informs  that on June 30, 2004,  the Supreme  Court,  New York County  entered a
decision and order  denying in its  entirety  the request of certain  holders of
2004 senior  notes that the Company be  preliminarily  enjoined  from selling or
otherwise  transferring certain assets. This in connection with the extension of
the lawsuit filed on January  2004,  by certain  holders of the Senior Notes due
2004 against our principal  subsidiary,  Grupo  Iusacell  Celular,  S.A. de C.V.
("Iusacell Celular") and others.

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

About Iusacell
--------------
Grupo  Iusacell,  S.A. de C.V.  (Iusacell,  NYSE:  CEL;  BMV: CEL) is a wireless
cellular  and  PCS  service   provider  in  Mexico   encompassing   a  total  of
approximately 92 million POPs,  representing  approximately 90% of the country's
total population.

Independently of the negotiations towards the restructure of its debt, Iusacell
reinforces its commitment with customers, employees and suppliers and guarantees
the highest quality standards in its daily operations offering more and better
voice communication and data services through state-of-the-art technology, as
the new 3G network, in more populations, thanks to its aggressive expansion
plan.

                                       ***

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.