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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 29, 2006

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 Iusacell Announces Extension

    MEXICO CITY, June 29 /PRNewswire-FirstCall/ -- Grupo Iusacell, S.A. de
C.V. (BMV: CEL) ("Iusacell") announced that due to the request of certain
creditors in the exchange offer of its principal operating subsidiary, Grupo
Iusacell Celular ("Iusacell Celular"), in respect of its US$190 million of
Tranche A Bank Loans (the "Tranche A Loans"), US$76 million of Tranche B Bank
Loans (the "Tranche B Loans") and US$150 million 10% Senior Notes due in 2004
(the "Existing Notes") which was launched on May 25, 2006, Iusacell Celular
has decided to extend the expiration date for such offer (the "Expiration
Date") to July 14, 2006.

    As was announced on May 25, 2006, and pursuant to the agreement reached
with the majority of its creditors, Iusacell Celular launched a solicitation
of consents to:

    -- exchange any and all of its Tranche A Loans for new senior floating
       rate first lien notes due 2011; and

    -- exchange any and all of its Tranche B Loans and its Existing Notes for
       10% senior subordinated second lien notes due 2012.

    THE EXCHANGE OFFER WILL EXPIRE AT 5:00PM, EDT, ON JULY 14, 2006, UNLESS
AGAIN EXTENDED BY IUSACELL.

    All references in the Information Memorandum dated May 25, 2006 to the
Expiration Date will include reference to such term as herein described.
Except as described above, the restructuring of the Existing Notes will remain
in all other respects subject to all terms and conditions described in the
Information Memorandum dated May 25, 2006.

    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.

    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.

    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.

SOURCE  Grupo Iusacell, S.A. de C.V.
    -0-                             06/29/2006
    /CONTACT:  Investors, Jose Luis Riera K., Chief Financial Officer,
+011-5255-5109-5927, or J.Victor Ferrer, Finance Manager, +011-5255-5109-5273,
or vferrer@iusacell.com.mx, both of Iusacell /
    /Web site:  http://www.iusacell.com /

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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 29, 2006

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

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

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