# 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 March, 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
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|For
      more information contact:                                              |                                                              
|-------------------------------------------------------------------------------- | -------------------------------------------------------------
|Dr. José Luis Guerrero
      (5255) 5272-9991 x2060jose.guerrero@ica.com.mx      | in
      the United States:
      Zemi Communications        
|Arq.
      Ana P. Fernandez
      (5255) 5272-9991 x3480ana.fernandez@ica.com.mx | Daniel
      Wilson
      (212) 689-9560d.b.m.wilson@zemi.com
|                                                                                 |                                                              

ICA
  ANNOUNCES CIVIL CONSTRUCTION CONTRACTS FOR MORE THAN Ps. 1,000 MILLION

Mexico City, March 29,
  2004  Empresas ICA Sociedad Controladora (NYSE and BMV: ICA),the
  largest engineering, procurement and construction company in Mexico, today announced
  that it has signed contracts of several projects with a value of more than Ps.
  1,000 million.

The first contract corresponds
  to the 6 km Tejocotal-Nuevo Necaxa section of the Mexico-Tuxpan highway, which
  totals Ps. 446 million, and includes the construction of landfills, drainage
  works, pavement, complementary works, as well as bridges and under bypasses.
  These works will be constructed over a period of 18 months.

The second contract relates
  to the Lopez Portillo interchange, which has a value of Ps. 180
  million, and comprises the construction of structures, landfills, pavement,
  drainage, and complementary works. Located in the EcatepecOjo de Agua
  section in the State of Mexico, it will be constructed over 13 months.

Both projects will be constructed
  for the Highway and Bridges Trust for the central Gulf region.

In a third contract, the Government
  of the Federal District, through the Secretary of Public Works and Services,
  awarded ICA the contract to build a Modular Specialty Hospital in the Iztapalapa
  district, with a capacity of 144 beds. The Ps. 350 million fixed price contract
  includes construction and equipment, and will be constructed over 11 months.
  The hospital will include obstetrics, perinatology, internal medicine, general
  surgery, auxiliary, and other services.

The final contract awarded
  to ICA corresponds to the manufacturing and partial storage of 2,167 concrete
  panels for the construction of the second stage of the VII, VIII, IX and X sections
  of the San Antonio distributor road system. The works would be done for the
  Government of the Federal District, through the Federal District Road System
  Improvement Trust (FIMEVIC). The fixed price Ps. 53 million contract will be
  executed over 5 months.







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|INVESTOR RELATIONS



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Founded in
  1947, ICA has completed construction and engineering projects in 21 countries.
  ICAs principal businessunits include Civil Construction and Industrial
  onstruction. Through its subsidiaries, ICA also manages airportsand operates
  tunnels, highways, and municipal services under government concession contracts
  and/or partial sale oflong-term contract rights.



































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|INVESTOR RELATIONS



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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: March
  29, 2004

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