Exhibit 99.1

[GRAPHIC]

For Immediate Release:

Contacts: Alexion Pharmaceuticals, Inc. David Keiser President & COO 203-272-2596 Euro RSCG Life NRP Ernie Knewitz (Media) 212-845-4253 Rx Communications Rhonda Chiger (Investor) 917-322-2569

Alexion Pharmaceuticals Reports Third Quarter and Nine Month Results

Cheshire, Conn., June 3, 2004 – Alexion Pharmaceuticals, Inc. (NASDAQ: ALXN) today announced financial results for its third fiscal quarter and nine months ended April 30, 2004.

For the quarter ended April 30, 2004, Alexion (the “Company”) reported revenues of $168,000 compared to $167,000 for the same period last year.

Total operating expenses for the quarter were $14.4 million compared to $19.4 million in the same quarter last year. The Company’s research and development expenses for the three-month period ended April 30, 2004 were $10.8 million compared to $14.1 million for the same period last year. The $3.3 million decrease resulted primarily from lower manufacturing development and manufacturing costs of approximately $5.7 million and lower discovery research costs of $0.8 million, partially offset by increased clinical development costs of $3.2 million. The decrease in manufacturing development and manufacturing costs is primarily a result of lower third-party manufacturing-related costs incurred in the current period primarily due to contract scheduling. The decrease in discovery research is primarily due to the suspension of the Unigraft xenotransplantation program at Columbus Farming Corporation (“CFC”) and lower external research and license fees. The increase in clinical development costs of $3.2 million is due principally to the timing of responsibility for costs incurred for pexelizumab related clinical trials. In the third quarter of the prior fiscal year, Procter & Gamble Pharmaceuticals (“P&G”) was primarily responsible for costs associated with the Phase III PRIMO-CABG clinical trials. In the third quarter of the current fiscal year, the Company and P&G shared equally in the costs of pexelizumab related clinical trials. Since the first quarter of fiscal year 2004, per our collaboration, the Company and P&G shared concurrently 50% of the on-going U.S. pre-production and development manufacturing costs for pexelizumab as well as the Phase III AMI and Phase III CABG clinical trial costs. The Company’s general and administrative expenses were $3.6 million for the three months ended April 30, 2004 compared to $2.7 million for the same period last year. This $0.9 million increase resulted principally from increased expenses associated with pre-marketing and business development activities, as well as increased personnel and professional services to support the continued growth of the Company’s operations. During the quarter ended April 30, 2003, the Company also recorded an impairment of fixed assets charge of $2.6 million related to a significant change in the manner in which CFC was utilizing its Unigraft facility and related assets as a result of the suspension of the Unigraft xenotransplantation program.

The Company posted investment income for the quarter of $720,000 compared to $1.2 million for the same period last year, reflecting lower principal and lower market interest rates. 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 recorded a state tax benefit of approximately $186,000 for the quarter ended April 30, 2004 and a benefit of $196,000 in the quarter ended April 30, 2003. The benefit is the result of legislation by the State of Connecticut that allows for exchange of research and development tax credits for cash.

The Company incurred a net loss for the quarter of $15.2 million, or $0.69 per common share, versus a net loss of $19.8 million, or $1.09 per common share, for the same three-month period in 2003.

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For the nine months ended April 30, 2004 the Company’s revenues were $462,000 compared to $710,000 for the same period ended April 30, 2003. The decrease in revenue as compared to the same period a year ago resulted primarily from the reduction in grant reimbursable billings as a result of completion of the related research.

Total operating expenses were $51.7 million and $62.7 million for the nine months ended April 30, 2004 and 2003, respectively. Research and development expenses were $42.0 million for the nine months ended April 30, 2004 compared to $52.5 million for the nine months ended April 30, 2003. The $10.5 million decrease resulted primarily from lower clinical development costs of $9.6 million and lower discovery research costs of approximately $2.9 million. The decrease in clinical development costs was due principally to the completion of the pexelizumab Phase III PRIMO-CABG clinical study. The decrease in research discovery was due principally to lower research and license fees and the suspension of the Unigraft program at CFC. Partially offsetting the decrease in clinical development and research discovery costs were increased manufacturing development and activity costs of approximately $900,000 and increased headcount and compensation costs of approximately $1.3 million. General and administrative expenses were $9.7 million for the nine months ended April 30, 2004 and $7.7 million for the nine months ended April 30, 2003. This $2.0 million increase resulted principally from increased expenses associated with pre-marketing and business development activities, as well as increased personnel and professional services to support the continued growth of the Company’s operations. The Company recorded an impairment of fixed assets charge of $2.6 million during the quarter ended April 30, 2003 related to the suspension of the Unigraft xenotransplantation program.

Investment income was $2.7 million for the nine months ended April 30, 2004 and $4.7 million for the nine months ended April 30, 2003. The decrease in investment income of $2.0 million resulted primarily from lower principal and lower market interest rates. Interest expense, primarily on the Company’s $120 million convertible subordinated notes, was $5.8 million for the nine months ended April 30, 2004 and 2003. For the nine months ended April 30, 2004, the Company recorded a state tax benefit of approximately $319,000. The benefit is the result of legislation by the State of Connecticut that allows for exchange of research and development tax credits for cash.

As a result of the above factors, the Company incurred a net loss of $54.0 million, or $2.54 basic and diluted net loss per common share, for the nine months ended April 30, 2004 compared to a net loss of $62.9 million, or $3.45 basic and diluted net loss per common share, for the nine months ended April 30, 2003.

Certain reclassifications have been made to prior year operating expenses for the three and nine months ended April 30, 2003 to conform prior year expense classifications to current year expense classifications.

As of April 30, 2004, Alexion had approximately $204.2 million in cash, cash equivalents and marketable securities.

Based on the nine month results and following further prioritization of R&D efforts and scheduling of manufacturing activities, management’s guidance for the net loss for the year ending July 31, 2004, subject to the actual timing of revenues related to certain development milestones, is now expected to be lower and in a range of $80 to $85 million versus the $83 to $96 million range previously cited.

“Our third quarter was highlighted by the publication of the results of our first Phase III clinical trial of pexelizumab, known as PRIMO-CABG, in the Journal of the American Medical Association (“JAMA”). This, together with the recent publication of eculizumab PNH results in the New England Journal of Medicine, elevates the interest and support for both drugs as we undertake their respective Phase III pivotal trials,” said David Keiser, President and Chief Operating Officer of Alexion. “We are very focused on carrying out our three Phase III programs which include eculizumab in PNH patients and pexelizumab in CABG surgery patients and in myocardial infarction patients receiving angioplasty. We believe this represents a unique platform of late stage development and commercial opportunities.”

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Alexion is engaged in the discovery and development of therapeutic products aimed at treating patients with a wide array of severe disease states, including cardiovascular and autoimmune disorders, inflammation and cancer. Alexion’s two lead product candidates, pexelizumab and eculizumab, are currently undergoing evaluation in several clinical development programs. Alexion has completed a Phase III clinical study with pexelizumab in CABG patients undergoing cardiopulmonary bypass, and two large Phase II studies with pexelizumab in acute myocardial infarction patients. The Phase III trial and Phase II trials were conducted in collaboration with Procter & Gamble Pharmaceuticals. In addition, eculizumab has completed Phase II clinical trials in rheumatoid arthritis and membranous nephritis, and has completed pilot programs for the treatment of paroxysmal nocturnal hemoglobinuria and dermatomyositis. 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 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 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, 2003, as amended and in our other filings with the Securities and Exchange Commission. 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.

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ALEXION PHARMACEUTICALS, INC.

Selected Financial Data

Statements of Operations (unaudited)

(amounts in thousands, except per share amounts)

	Three months ended April 30,						Nine months ended April 30,
	2004			2003			2004			2003
CONTRACT RESEARCH REVENUES	$	168		$	167		$	462		$	710
OPERATING EXPENSES
Research and development		10,792			14,110			42,004			52,454
General and administrative		3,569			2,732			9,683			7,727
Impairment of fixed assets		—			2,560			—			2,560
Total operating expenses		14,361			19,402			51,687			62,741
Operating loss		(14,193	)		(19,235	)		(51,225	)		(62,031	)
OTHER INCOME AND EXPENSE
Investment income		720			1,191			2,715			4,735
Interest expense		(1,926	)		(1,930	)		(5,781	)		(5,783	)
Loss from operations before taxes		(15,399	)		(19,974	)		(54,291	)		(63,079	)
State tax benefit		186			196			319			196
Net loss	$	(15,213	)	$	(19,778	)	$	(53,972	)	$	(62,883	)
BASIC AND DILUTED NET LOSS PER SHARE	$	(0.69	)	$	(1.09	)	$	(2.54	)	$	(3.45	)
SHARES USED IN COMPUTING BASIC AND DILUTED NET LOSS PER COMMON SHARE		21,969			18,210			21,268			18,207
Balance Sheet Data (dollars in thousands)
				Apr 30, 2004			Apr 30, 2003			July 31, 2003
				(unaudited)			(unaudited)			(audited)
Cash, cash equivalents and marketable securities				$	204,173		$	230,935		$	215,410
Total Assets				$	253,265		$	282,043		$	266,077
Net Stockholders’ Equity				$	111,862		$	142,396		$	120,286

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