Exhibit 99.1

CHESHIRE, Conn., Dec. 3 /PRNewswire-FirstCall/ — Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) today announced financial results for its first fiscal quarter ended October 31, 2004. Alexion (the Company) reported revenues amounting to $147,000 for the first quarter ended October 31, 2004. This matched revenues of $147,000 reported for the same period last year.

Total operating expenses for the quarter were $22.3 million, compared to $19.5 million for the same quarter last year. The Company’s research and development expenses for the three-month period ended October 31, 2004 were $18.7 million compared to $16.7 million for the same period last year. The $2.0 million increase in research and development expenses resulted primarily from higher clinical development costs of approximately $1.3 million related to the three ongoing Phase III clinical trials of the Company’s lead compounds pexelizumab and eculizumab, higher discovery research costs of approximately $140,000 principally due to higher external research and licensing fees, increased headcount resulting in higher payroll and benefits costs of approximately $290,000, higher manufacturing development and manufacturing activities of approximately $200,000, and increased occupancy and depreciation costs of approximately $90,000. The Company’s general and administrative expenses were $3.7 million for the three-months ended October 31, 2004 compared to $2.8 million for the three-months ended October 31, 2003. The $865,000 increase resulted principally from heightened pre-marketing and business development activities in support of our PNH development programs, as well as increased personnel and professional services to support the continued growth of the Company’s operations.

The Company posted investment income of $1.0 million for the first quarter of fiscal 2005, which equals the same amount posted in the first quarter of fiscal 2004. Interest expense, primarily on the Company’s $120 million convertible subordinated notes, was unchanged at $1.9 million for the quarter compared to the same period last year. The Company also recorded a net gain of $3.8 million to complete the termination of the Unigraft xenotransplantation program at its Columbus Farming Corporation subsidiary. The net gain was realized as a result of extinguishing the $3.9 million note payable used to purchase the xenotransplantation assets from U.S. Surgical Corporation, now a division of Tyco International, Ltd. (Tyco), and from extinguishing the accrued interest of $0.3 million on the note, partially offset by the transfer to Tyco of the remaining assets of $450,000 used to originally secure the note. The Company recorded a State tax benefit of approximately $62,000 for the quarter ended October 31, 2004 and a benefit of $71,000 in the quarter ended October 31, 2003. The benefit is the result of legislation by the State of Connecticut that allows for exchanging research and development tax credits for cash.

After accounting for its one-time net gain of $3.8 million to complete the termination of the Unigraft xenotransplantation program at its Columbus Farming Corporation subsidiary, Alexion incurred a net loss for the quarter of $19.2 million, or $0.70 per share versus a net loss of $20.2 million or $1.01 per common share for the same three-month period in 2003.

As of October 31, 2004, Alexion had approximately $246.8 million in cash, cash equivalents and marketable securities.

“Our first quarter results reflect our progress in aggressively moving forward with our three ongoing Phase III clinical programs; led by eculizumab in PNH and pexelizumab in both coronary artery bypass graft surgery patients and acute myocardial infarction patients receiving angioplasty,” said David W. Keiser, President and Chief Operating Officer of Alexion. “This past quarter was noteworthy for the commencement of the TRIUMPH pivotal PNH trial which we expect to complete in 2005. Further, as our ongoing pivotal Phase III PRIMO- CABG2 study is focused on coronary

artery bypass graft surgery patients with multiple risk factors and includes valve patients, we are encouraged by the recent data presented last month at the American Heart Association Meeting which indicated that the pexelizumab Death/MI benefit is consistent and enhanced in patients with specific and/or multiple baseline risk factors. We look forward to the completion of this important trial which is anticipated during the second half of 2005.”

Alexion is engaged in the discovery and development of therapeutic products aimed at treating patients with a wide array of severe disease states, including hematologic and cardiovascular disorders, autoimmune diseases and cancer. Alexion’s two lead product candidates, pexelizumab and eculizumab, are currently undergoing evaluation in several clinical development programs, including two Phase III trials of eculizumab for the treatment of paroxysmal nocturnal hemoglobinuria (PNH), a Phase III trial of pexelizumab in coronary artery bypass graft (CABG) surgery patients undergoing cardiopulmonary bypass (CPB), and a Phase III trial of pexelizumab in acute myocardial infarction (AMI) patients. The pexelizumab trials are conducted in collaboration with Procter and Gamble Pharmaceuticals. Under the Special Protocol Assessment process, the FDA has agreed to the design of protocols for the Phase III pexelizumab trials that could, if successful, serve as the primary basis of review for approval of Biologics License Applications for the two indications. Eculizumab has completed a pilot clinical trial for the treatment of paroxysmal nocturnal hemoglobinuria (PNH). Under the Special Protocol Assessment process, the FDA has agreed to the design of protocols for the two trials of eculizumab in PNH patients that could, if successful, serve as the primary basis of review for approval of a Biologics License Application for eculizumab in the PNH indication. Eculizumab is also in Phase II clinical development in rheumatoid arthritis and membranous nephritis. Alexion is engaged in discovering and developing a pipeline of additional antibody therapeutics targeting severe unmet medical needs, through its wholly owned subsidiary, Alexion Antibody Technologies, Inc. This press release and further information about Alexion Pharmaceuticals, Inc. can be found on the World Wide Web at: http://www.alexionpharm.com

This news release contains forward-looking statements. Such statements are subject to factors that may cause Alexion’s results and plans to differ from those expected, including the results of pre-clinical or clinical studies (including termination or delay in clinical programs), the need for additional research and testing, delays in arranging satisfactory manufacturing capability, inability to acquire funding on timely and satisfactory terms, delays in developing or adverse changes in commercial relationships, the possibility that results of earlier clinical trials are not predictive of safety and efficacy results in later clinical trials, dependence on Procter & Gamble Pharmaceuticals (P&GP) for development and commercialization of pexelizumab, the risk that third parties won’t agree to license any necessary intellectual property to us on reasonable terms, and a variety of other risks set forth from time to time in Alexion’s filings with the Securities and Exchange Commission, including but not limited to the risks discussed in Alexion’s Annual Report on Form 10-K for the year ended July 31, 2004. P&GP retains the development rights and the termination rights discussed in Alexion’s Form 10-K referred to above. Alexion does not intend to update any of these forward-looking statements to reflect events or circumstances after the date hereof, except when a duty arises under law.

ALEXION PHARMACEUTICALS, INC.

Selected Financial Data

Statements of Operations (unaudited)

(amounts in thousands, except per share amounts)

	Three months ended October 31,
	2004			2003
CONTRACT RESEARCH REVENUES	$	147		$	147
OPERATING EXPENSES
Research and development		18,663			16,688
General and administrative		3,679			2,814
Total operating expenses		22,342			19,502
Operating loss		(22,195	)		(19,355	)
OTHER INCOME AND EXPENSE
Investment income		1,049			1,001
Interest expense		(1,908	)		(1,929	)
Gain from extinguishment of note payable		3,804			—
Loss before income tax benefit		(19,250	)		(20,283	)
STATE INCOME TAX BENEFIT		62			71
Net loss	$	(19,188	)	$	(20,212	)
BASIC AND DILUTED NET LOSS PER SHARE	$	(0.70	)	$	(1.01	)
SHARES USED IN COMPUTING BASIC AND DILUTED NET LOSS PER COMMON SHARE		27,607			19,958

Balance Sheet Data

(dollars in thousands)

	October 31, 2004 (unaudited)		July 31, 2004 (audited)
Cash, cash equivalents and marketable securities	$	246,792	$	266,501
Total Assets	$	297,412	$	319,575
Net Stockholders’ Equity	$	153,960		172,522

Alexion Pharmaceuticals, Inc.

David Keiser

President & COO

203-272-2596

Euro RSCG Life NRP

Robert Stanislaro (Media)

212-845-4268

Rx Communications

Rhonda Chiger (Investor)

917-322-2569