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 January, 2004

                          GRUPO IUSACELL, S.A. de C.V.

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                 (Translation of registrant's name into English)

                         Prol. Paseo de la Reforma 1236
                        Col. Santa Fe, Deleg. Cuajimalpa
                               05438, 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 January 23, 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: January 19, 2004              /s/     Jose Luis Riera
                                    --------------------------------------
                                            Name:  Jose Luis Riera
                                            Title: Attorney in fact

                                    /s/     Fernando Cabrera G.
                                    --------------------------------------
                                            Name:  Fernando Cabrera G.
                                            Title: Attorney in fact


[LOGO] IUSACELL
         Valora tu espacio.
                                                               INVESTOR CONTACTS

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

                                                             Carlos J. Moctezuma
                                                      Head of Investor Relations
                                                                  5255-5109-5759
                                                carlos.moctezuma@iusacell.com.mx

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Iusacell Announced
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Mexico City,  January 23, 2004 - Grupo Iusacell,  S.A. de C.V., [BMV: CEL, NYSE:
CEL], today announced that in December 2003 its main operating  subsidiary Grupo
Iusacell  Celular,  S.A.  de C.V.  and  certain  of its  subsidiaries  (Iusacell
Celular), entered a series of agreements with the Mexican subsidiary of American
Tower  Corporation  (MATC)  that,  among other  things,  gives MATC the right to
acquire up to 143 existing Iusacell Celular towers over the course of this year.
In  accordance  with the  agreements,  Iusacell  Celular  is in the  process  of
transferring  its  towers  to  MATC.   Iusacell  Celular  will  then  lease  the
transferred towers back from MATC.

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

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.