SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, DC 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER
PURSUANT TO RULE 13a-16 OR 15d-16 OF
THE SECURITIES EXCHANGE ACT OF 1934

For the month of May 2004

Commission File Number 1-14858

CGI Group Inc.
(Translation of Registrant’s Name Into English)

1130 Sherbrooke Street West
5th Floor
Montréal, Québec
Canada H3A 2M8
(Address of Principal Executive Offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F    Form 40-F |X|

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): ____

Note: Regulation S-T Rule 101(b)(1) only permits the submission in paper of a Form 6-K if submitted solely to provide an attached annual report to security holders.

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): ____

Note: Regulation S-T Rule 101(b)(7) only permits the submission in paper of a Form 6-K if submitted to furnish a report or other document that the registrant foreign private issuer must furnish and make public under the laws of the jurisdiction in which the registrant is incorporated, domiciled or legally organized (the registrant’s “home country”), or under the rules of the home country exchange on which the registrant’s securities are traded, as long as the report or other document is not a press release, is not required to be and has not been distributed to the registrant’s security holders, and, if discussing a material event, has already been the subject of a Form 6-K submission or other Commission filing on EDGAR.

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 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-___.

Enclosure: Press Release dated May 20, 2004.

This Form 6-K shall be deemed incorporated by reference in the Registrant's Registration Statement on Form S-8, Reg. Nos. 333-13350, 333-66044, 333-74932 and 333-112021.

PRESS RELEASE FOR IMMEDIATE RELEASE

Cox outsources its IT department to CGI in 10-year contract
valued at £138 million

London, UK, May 20, 2004 – Information technology (IT) and business process services firm, CGI Group (Europe) Limited, part of CGI Group Inc. (CGI) (TSX: GIB.A; NYSE: GIB) today announced that Cox Insurance Holdings Plc, one of the largest motor insurers in the UK, has signed a full, end-to-end, ten-year IT outsourcing contract with CGI valued at £138 million (CDN $338 million, US $246 million).

As part of the contract, CGI will become the primary manager of all aspects of the insurer’s computing infrastructure, providing applications management including support and maintenance, and development activities spanning Cox’s entire business. Under this agreement, more than 200 Cox professionals are transferring to CGI under TUPE – Transfer of Undertaking (Protection of Employment). CGI will capitalize upon its position as a global services company by providing Cox with more efficient, cost effective services through the use of its UK and offshore facilities in Canada and India.

Neil Utley, CEO of Cox Insurance Holdings Plc, commented: “Working with CGI, we will be able to stay focused on the core competency of our insurance business while benefiting from CGI’s expertise and best-of-breed technology services. CGI is a company able to provide the thought leadership and strategic focus we are looking for in a services provider.”

Cox is a long-term customer of CGI’s, having worked with its back-office administration solution, Real-time Transaction Manager (RTM), for over 20 years. Gavin Chapman, senior vice-president and managing director of CGI in Europe, said: “Our close working relationship over the years has demonstrated to Cox that CGI is able to provide the necessary expertise, flexibility and risk management to bring significant value to Cox’s business through a relationship of this kind. CGI’s rapidly expanding UK operations enables us to build our business around key partners, such as Cox.”

Utley continued: “Cox will realize a number of benefits from outsourcing its IT services to CGI. Not only will it enable Cox to exploit technology to reduce the cost of its business processes, it will also improve service levels and flexibility and provide Cox with the advantage of having a single point of contact for all IT related issues. The transfer of our professionals to an IT provider that is highly focused on our marketplace will also bring about greater career opportunities for them.”

Michael Roach, president and chief operating officer for CGI added: “We are extremely pleased to welcome our new professionals to the team and to broaden our relationship with Cox. This contract further underlines our strength and global capability in the financial services sector, supporting our strategic growth plans within the European insurance industry. In building our critical mass in the UK in insurance, we are strengthening our foothold in areas that are increasingly competitive. Outsourcing provides a clear path for companies wanting to maintain and increase their competitive advantage.”

About Cox Insurance Holdings Plc
Cox Insurance Holdings Plc is a leading company in the UK retail insurance market. The group combines the largest motor underwriter at Lloyd’s with a growing broking and insurance services business. Cox is the UK’s largest insurer of motorcycles and the seventh biggest motor insurer. Cox’s integrated business model, its highly selective underwriting criteria and mix of distribution channels are the differentiating factors that will continue to drive growth and deliver shareholder value. For further information visit Cox at www.cox.co.uk

About CGI
Founded in 1976, CGI is among the largest independent information technology and business process services firms in North America. CGI and its affiliated companies employ approximately 25,000 professionals. CGI provides end-to-end IT and business process services to clients worldwide from offices in Canada, the United States, Europe, Asia Pacific as well as from centers of excellence in India and Canada. CGI’s annualized revenue run rate is currently CDN$3.8 billion (US$2.8 billion) and at March 31, 2004, CGI’s order backlog was CDN$12.0 billion (US$9.1 billion). CGI’s shares are listed on the TSX (GIB.A) and the NYSE (GIB) and are included in the S&P/TSX Composite Index as well as the S&P/TSX Capped Information Technology and MidCap Indices. Website: www.cgi.com.

Forward-Looking Statements
All statements in this press release that do not directly and exclusively relate to historical facts constitute “forward-looking statements” within the meaning of that term in Section 27A of the United States Securities Act of 1933, as amended, and Section 21E of the United States Securities Exchange Act of 1934, as amended. These statements represent CGI Group Inc.‘s intentions, plans, expectations, and beliefs, and are subject to risks, uncertainties, and other factors, of which many are beyond the control of the Company. These factors could cause actual results to differ materially from such forward-looking statements.

These factors include and are not restricted to the timing and size of contracts, acquisitions and other corporate developments; the ability to attract and retain qualified employees; market competition in the rapidly-evolving information technology industry; general economic and business conditions, foreign exchange and other risks identified in the Management’s Discussion and Analysis (MD&A) in CGI Group Inc.‘s Annual Report or Form 40-F filed with the SEC, the Company’s Annual Information Form filed with the Canadian securities authorities, as well as assumptions regarding the foregoing. The words “believe”, “estimate”, “expect”, “intend”, “anticipate”, “foresee”, “plan”, and similar expressions and variations thereof, identify certain of such forward-looking statements, which speak only as of the date on which they are made. In particular, statements relating to future revenue from outsourcing contracts are forward-looking statements. CGI disclaims any intention or obligation to publicly update or revise any forward-looking statements, whether as a result of new information, future events or otherwise. Readers are cautioned not to place undue reliance on these forward-looking statements.

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For more information:

UK ENQUIRIES:

Cox
Neil Utley
Chief Executive
Cox Insurance Holding Plc
(44) 01277 206103

Rachel Hirst/John Olsen
Hogarth Partnership
(44) 020 7357 9477

CGI
Lisa Carter/Louisa Constable
Portfolio Communications Ltd
(44) 020 7240 6959

NORTH AMERICAN ENQUIRIES:

CGI Investor relations
Julie Creed
Vice-president, investor relations
(312) 201-4803

Ronald White
Director, investor relations
(514) 841-3230

CGI Media relations
Eileen Murphy
Director, media relations
(514) 841-3430

SIGNATURES

       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.

	CGI GROUP INC.     (Registrant)
Date:    May 21, 2004	By /s/ Paule Doré        Name:   Paule Doré        Title:     Executive Vice-President                      and Chief Corporate Officer                      and Secretary