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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 __ March, 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 March 20, 2006

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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: March 20, 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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[LOGO OF IUSACELL]                                             INVESTOR CONTACTS
        PENSAMOS EN TI
                                                              Jose Luis Riera K.
                                                         Chief Financial Officer
                                                                  5255-5109-5927

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

IUSACELL ANNOUNCES:

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Mexico City, March 20, 2006 - Grupo Iusacell, S.A. de C.V. [BMV: CEL]
("Iusacell") announced today that it has agreed with the majority of the holders
of its US$350 million 14.25% notes due in 2006 (the "Existing Notes") to extend
the time for the launch of the exchange offer and consent solicitation for the
amendment of certain terms and conditions of the Existing Notes and the waiver
of certain events under such notes, all of which is intended to be done to
implement the agreements in principle reached with those creditors and
previously announced. Iusacell currently contemplates launching the exchange
offer and consent solicitation on or before April 19, 2006.

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

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.

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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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