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                                  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, 2005

                          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]

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Documents Furnished By the Registrant

1.   Press Release of the Registrant dated May 6, 2005

                                   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 6, 2005                                     /s/ Fernando Cabrera
                                                      --------------------------
                                               Name:  Fernando Cabrera
                                               Title: Attorney in fact

                                                      /s/ Jose Luis Riera
                                                      --------------------------
                                               Name:  Jose Luis Riera
                                               Title: Attorney in fact



[LOGO OF 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

IUSACELL ANNOUNCEMENT

Mexico City, May 6, 2005 - Grupo Iusacell, S.A. de C.V., [BMV: CEL, NYSE: CEL],
announced that in regards to a May 3 press release concerning receipt of a
notice from the Trustee Agent of the Bond due in 2006, the notice does not
affect discussions nor does it alter the debt restructuring process.

Grupo Iusacell reiterates its commitment to continue negotiations with creditors
to try to reach a comprehensive restructuring agreement as soon as possible.

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

ABOUT IUSACELL

Grupo Iusacell, S.A. de C.V. (Iusacell, NYSE and 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. Independent of the negotiations towards the restructuring 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, such as its new 3G network, throughout all of the
regions in which it operate.

LEGAL DISCLAIMER

Grupo Iusacell, S.A. de C.V. quarterly reports 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.