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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 2, 2005

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                                   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 2, 2005                                   /s/ Fernando Cabrera
                                                    --------------------
                                            Name:   Fernando Cabrera
                                            Title:  Attorney in fact

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

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                                                               INVESTOR CONTACTS
[LOGO OF IUSACELL]
   PENSAMOS EN TI                                             Jose Luis Riera K.
                                                         Chief Financial Officer
                                                                  5255-5109-5927

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

Grupo Iusacell will Convene an Extraordinary Shareholders Meeting to Consider
the Convenience to Continue with its American Depositary Shares Program

        Mexico City, May 2, 2005 - Grupo Iusacell, S.A. de C.V., [BMV: CEL,
NYSE: CEL], announced today that it will submit to the consideration of an
extraordinary shareholders meeting the convenience to continue with its American
Depository Shares (ADSs) program in the United States with shares listed in the
New York Stock Exchange (NYSE).

        The Company considers that renowned cases of regulatory non-compliance
in the recent past, such as Worldcom, Enron, Adelphia, Parmalat, etc. have
created over-regulation in the United States securities markets. As a result,
issuers have had to divert time and resources to comply with excessive
regulation, to the detriment of a more efficient management of the business.

        For foreign issuers in the United States, over-regulation considerably
increases current costs and expenses, along with the risk of liability, and the
benefits are very questionable. As a result of this, the shareholders meeting of
Grupo Iusacell will consider the impact of the costs upon its business, as well
as the current and future benefits of its ADSs program.

        If the shareholders' meeting decides to terminate the ADSs program, the
Company would disclose it to investors and would send notice of this decision to
Bank of New York (BONY). Pursuant to section 6.02 of the Deposit Agreement
signed with BONY, the Company has the power to terminate it. This contract can
be accessed in documents filed by the Company with the Securities & Exchange
Commission (SEC) or in http://www.sec.gov/Archives/edgar/data/1089695
/000101915503000504/0001019155-03-000504-index.htm. Such termination would be
notified to ADSs holders 90 days in advance of its termination.

        If the shareholders meeting decides to terminate the ADSs program: a)
the Company would immediately communicate this decision to both BONY and the New
York Stock Exchange (NYSE); b) BONY would notify holders of ADSs; c) the Company
would proceed to modify its F-6 format (ADSs Registry), reducing the issuance of
ADSs to zero; and d) the Company would file its modified F-6 form with the SEC.

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        Trading of ADSs may continue during the 90 days following the
termination of the Deposit Agreement. During that period, ADSs holders may
continue to exchange them for common shares listed on the Mexican Stock Exchange
(BMV).

        Once the Deposit Agreement is terminated, the NYSE should suspend the
trading of ADSs, should notify the SEC of the termination of the program, and
request the delisting of the ADSs from the NYSE. In case that the delisting from
the NYSE were to happen, the SEC would make it public.

        In that case, ADSs holders would have the following two options during
the period of time determined by the shareholders meeting: 1) Give instructions
to BONY to exchange its ADSs into common shares, or 2) exchange their ADSs into
common shares and request their sale in the Mexican market.

        If there are less than 300 holders who are residents of the United
States, the Company may ask the SEC to cancel the registration of the ADSs. In
that case, the reporting obligations and other U.S. securities regulatory
compliance requirements would cease to apply to the Company. We must highlight
that the registry with the SEC and the listing with the NYSE are two independent
acts, and as such, in case of an eventual delisting from the NYSE, the Company
would continue complying with its reporting obligations with the SEC, for as
long as its registry with this authority is maintained.

        The trading of shares in Mexico and the United States will remain in
place until the shareholders meeting decides about it.

        If the shareholders' meeting decides not to terminate the ADSs program,
the Company would maintain its outstanding stock in the US market as it is
today, and ADSs holders would maintain the same rights they currently possess.

        In any event, the Company will timely disclose to investors the relevant
events that take place.

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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.

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