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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, 2006

                          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
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1.  Press Release of the Registrant dated May 25, 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 EXCHANGE OFFER

MEXICO CITY, MAY 25, 2006 - Grupo Iusacell, S.A. de C.V. [BMV: CEL] announced
today that its principal operating subsidiary Grupo Iusacell Celular ("Iusacell
Celular"), in accordance with an agreement reached with its majority creditors
(the "Majority Creditors") holding approximately 58% of our indebtedness, which
includes US$190 million of Tranche A Bank Loans, US$76 million of Tranche B Bank
Loans and US$150 million of 10% Senior Notes due in 2004, launched a
solicitation of consents to exchange any and all of its Tranche A Bank Loans for
new senior floating rate first lien notes due 2011 accruing interest at
three-month LIBOR plus 4.00% and its Tranche B Bank Loans and its Senior Notes
for its new 10% senior subordinated second lien notes due 2012, on the terms and
conditions that were previously announced in its press release dated January 23,
2006.

Iusacell Celular intends to effect the exchange through (i) a voluntary
exchange, or (ii) the filing of a plan of reorganization (convenio concursal)
pursuant to the Mexican Business Reorganization Act (Ley de Concursos
Mercantiles).

The Majority Creditors have agreed, subject to certain conditions, to timely
tender their indebtedness and grant their consents in the exchange offer.

Consummation of the offer is subject to certain customary conditions. The offer
is only made, and copies of any documents related thereto will only be made
available, to holders of Existing Debt that certify to Iusacell Celular that
they are eligible to participate in the offer.

THE EXCHANGE OFFER WILL EXPIRE AT 5:00 PM, NEW YORK CITY TIME, ON JUNE 29, 2006,
UNLESS EXTENDED BY IUSACELL CELULAR.

The Information and Exchange Agent for the exchange offer is Bondholder
Communications Group. The Information and Exchange Agent can be reached by email
at icolon@bondcom.com, and its telephone numbers are (44) 207-382-4580 in London
or 212-809-2663 in New York.

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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.

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Forward-Looking Statements

This release may contain forward-looking statements. Any such forward-looking
statements, which reflect Iusacell's current views of future events and
financial performance, involve known and unknown risks and uncertainties that
may cause Iusacell's actual results to be materially different from planned or
expected results. These risks and uncertainties include, but are not limited to,
competition, consumer demand, seasonality, economic conditions, and government
activity. Investors should take such risks into account when making investment
decisions.

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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 25, 2006

                                                    By:    /s/ Fernando Cabrera
                                                           ---------------------
                                                    Name:  Fernando Cabrera
                                                    Title: Attorney in fact


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

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