Exhibit 99.1

For Immediate Release:

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

ALEXION PHARMACEUTICALS APPOINTS CARSTEN BOESS

VICE PRESIDENT AND CHIEF FINANCIAL OFFICER

Cheshire, Conn, February 11, 2004 – Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) today announced the appointment of Carsten Boess as Vice President and Chief Financial Officer, a newly created position. Mr. Boess joins Alexion from Novo Nordisk International Operations where he most recently held the position of Vice President of Finance and also served as Chairman of Novo Nordisk’s International Operations Finance Board. Reporting to David Keiser, Mr. Boess will be responsible for all areas of accounting, finance, and administration, from operational and strategic viewpoints.

“We are very pleased to have Carsten join Alexion’s management team,” said David Keiser, President and Chief Operating Officer. “His extensive experience, in the U.S. and abroad, in all areas of accounting and finance within the pharmaceutical industry will be a tremendous asset to our organization as we move into the next phases of Alexion’s development and prepare for operating in a product revenue generating environment.”

Mr. Boess began his career at Novo Nordisk in 1991 as Corporate Controller. Subsequently he took on assignments with increasing responsibility including, at one time, Manager Investor Relations and Finance for Novo Nordisk North America, based in New York, as well as Senior Director Finance and IT of Novozymes’ North American operations. Mr. Boess holds Bachelor’s and Master’s degrees in economics and finance from the University of Odense, Denmark.

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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 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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