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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 June, 2006

                          GRUPO IUSACELL, S.A. de C.V.
                 -----------------------------------------------
                 (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
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1. Press Release of the Registrant dated June 2, 2006

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                                                               Investor Contacts

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

                                                                 J.Victor Ferrer
                                                                 Finance Manager
                                                                  5255-5109-5273
                                                         vferrer@iusacell.com.mx

GRUPO IUSACELL ANNOUNCES EXPIRATION OF EXCHANGE OFFER AND CONSENT SOLICITATION
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Mexico City, June 2, 2006 - Grupo Iusacell, S.A. de C.V. [BMV: CEL] ("Iusacell")
announced today the expiration on June 1, 2006 of the exchange offer and consent
solicitation relating to the restructuring (the "Restructuring") of its U.S.$350
million 14.25% notes due 2006 (the "Existing Notes") on the terms previously
announced in its press release dated January 23, 2006 and as described in
greater detail in its Information Memorandum dated April 18, 2006, as
supplemented on May 18, 2006 (the "Information Memorandum"). The Restructuring
contemplates that new notes will be issued in the principal amount of U.S.$175
million and will bear interest at an annual rate of 10% with semi-annual
interest payments (with Iusacell having the option to capitalize up to 40% of
each interest payment) (the "New Notes"). The New Notes will have a maturity
date of December 31, 2013 and its terms and conditions are expected to be as
described in the Information Memorandum.

     As of the expiration of the exchange offer and consent solicitation,
approximately 89% of the holders of the Existing Notes tendered their Existing
Notes. The participation of the holders of the Existing Notes demonstrated their
support of the agreements reached with a majority of Iusacell's creditors that
was previously announced in the press release dated January 23, 2006.

     "The results of the exchange offer and consent solicitation represent the
achievement of another milestone in the restructuring of Iusacell's debt and a
step towards the continued strengthening of our operations," commented Gustavo
Guzman, Chief Executive Officer of Iusacell.

     Iusacell also announced its decision to implement the Restructuring by the
filing of a plan of reorganization (convenio concursal) (the "Plan of
Reorganization") pursuant to the Mexican Business Reorganization Act (Ley de
Concursos Mercantiles). To implement its decision, and as part of the
restructuring process, Iusacell today filed for concurso mercantil, and will in
due course provide further information to its creditors relating to the Plan of
Reorganization and the concurso mercantil proceedings in accordance with the
Mexican Business Reorganization Act. Once the Plan of Reorganization is
presented to, and approved by the Mexican court and the terms and conditions of
the Restructuring are met, all Existing Notes will be exchanged for New Notes.

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     During the pendency of the concurso mercantil proceedings, Iusacell expects
that it and its subsidiaries will continue to operate normally.

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

THIS PRESS RELEASE IS NOT AN OFFER FOR SALE OF THE SECURITIES IN THE UNITED
STATES, MEXICO OR IN ANY OTHER JURISDICTION, AND NONE OF THE SECURITIES TO BE
ISSUED PURSUANT TO THE EXCHANGE OFFER, IF CONSUMMATED, MAY BE SOLD IN THE UNITED
STATES ABSENT REGISTRATION OR AN EXEMPTION FROM REGISTRATION UNDER THE
SECURITIES ACT OF 1933, AS AMENDED, OR IN ANY OTHER JURISDICTION WHERE SUCH SALE
IS PROHIBITED. THE COMPANY DOES NOT INTEND TO REGISTER ANY OF THE SECURITIES TO
BE ISSUED PURSUANT TO THE EXCHANGE OFFER IN THE UNITED STATES OR TO CONDUCT A
PUBLIC OFFERING OF SUCH SECURITIES IN ANY JURISDICTION OTHER THAN THOSE AS IT
MAY FROM TIME TO TIME PUBLISH.

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

ABOUT IUSACELL

Grupo Iusacell, S.A. de C.V. (Iusacell, BMV: CEL) is a wireless cellular and PCS
service provider in Mexico with a national footprint. 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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                                   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: June 2, 2006

                                                   /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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