# FORM 6-K
SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549

# Report of Foreign Private Issuer

# Pursuant to Rule 13a-16
or 15d-16of the Securities Exchange Act of 1934

For the month
  of September, 2004Commission File Number 1-11080

THE ICA CORPORATION
HOLDING COMPANY(Translation of registrants name into English)

Minería No. #14511800 México D.F.
(Address of principal executive offices)

Form 20-F....X.....Form 40-F.........

Indicate by check mark if the
registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule
101(b)(1): ____ 

Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7): ____ 

Indicate by check mark whether by furnishing the information contained in this Form, the registrant is also thereby
furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the
Securities Exchange Act of 1934.

Yes ..... No...X...

If Yes is marked, indicate
below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-
________

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| | PRESS
        RELEASE
| | ---------------------
|

|For more information
        contact:
      Ing. Alonso Quintana(5255) 5272-9991 x3468alonso.quintana@ica.com.mx
      Lic. Paloma
        Grediaga(5255) 5272-9991 x3664paloma.grediaga@ica.com.mx | in the United States:
        Zemi Communications
      Daniel Wilson
        (212) 689-9560d.b.m.wilson@zemi.com
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -----------------------------------------------------------------------------------------------------------------



# CONSORTIUM LED BY ICA
FLUOR SIGNS A US$ 134 MILLION 
CONTRACT WITH PEMEX TO BUILD A MODULAR CRYOGENIC 
PLANT

Mexico City, September 24, 2004  Empresas ICA Sociedad Controladora, S.A. de C.V. (BMV and NYSE: ICA), the
largest engineering, construction, and procurement company in Mexico, and Fluor
Corporation (NYSE: FLR) announced today that PEMEX Gas and Basic Petrochemicals and a
consortium formed by ICA Fluor and Linde Plantas de Procesamiento, Inc. have signed a US$
134 million contract for the construction of a modular cryogenic plant in Reynosa,
Tamaulipas as well as a fuel storage and distribution terminal. The plant will have a
capacity of 200 million cubic feet per day of natural gas, and a propane recovery factor
of 98 percent.

The ICA Fluor-Linde consortium will
execute the project over a term of 20 months.

The design of this cryogenic
plant minimizes natural gas consumption by employing a liquids recovery unit with low
pressure loss and high energy efficiency, said Jorge Borja, the director general of
ICA Fluor. This project ratifies the commitment of ICA Fluor to provide our clients
solutions with a strong cost-benefit relation and protection for the environment.

Pemex Gas and Basic Petrochemicals
is a subsidiary of Petroleos Mexicanos, PEMEX, Mexicos national oil and gas company.

ICA Fluor is the leading
industrial engineering company in Mexico, dedicated to the engineering, procurement, and
construction of oil and gas processing plants, petrochemical, chemicals, cement,
manufacturing, automotive plants, as well as power generation and telecommunication
facilities.

ICA (BMV and NYSE: ICA) was
founded in México in 1947. ICA has completed construction and engineering projects
in 21 countries. ICAs principal business units include civil construction and
industrial construction. Through its subsidiaries, ICA also develops housing, manages
airports, and operates tunnels, highways, and municipal services under government
concession contracts and/or partial sale of long-term contract rights. For more
information, visitwww.ica.com.mx.

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| | PRESS RELEASE
| | -------------
|

Fluor Corporation (NYSE:FLR)
provides services on a global basis in the fields of engineering, procurement,
construction, operations, maintenance and project management. Headquartered in Aliso
Viejo, Calif., Fluor is a Fortune 500 company with revenues of almost US$ 9 billion in
2003. For more information, visit www.fluor.com.

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|**RELACIONES CON INVERSIONISTAS** | **www.ica.com.mx** | **2/2**
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SIGNATURE

Pursuant
to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused
this Report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: September 24,
  2004

| | Empresas ICA Sociedad Controladora,
S.A. de C.V.                                  
| | ----------------------------------------------------------------------------------
| |                                                                                   
| | /s/ JOSE LUIS GUERRERO
Name: Dr. José Luis Guerrero
Title: Vice President, Finance