SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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                                    FORM 8-K

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                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

         Date of Report (Date of earliest event reported): May 25, 1999

                          ALEXION PHARMACEUTICALS, INC.
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             (Exact Name of Registrant as Specified in its Charter)

         Delaware                       0-27756                 13-3648318
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(State or Other Jurisdiction          (Commission              (IRS Employer
     of Incorporation)                File Number)           Identification No.)

     25 Science Park, New Haven, CT                                06511
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(Address of Principal Executive Offices)                         (Zip Code)

       Registrant's telephone number, including area code: (203) 776-1790

                                 Not Applicable
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          (Former Name or Former Address, if Changed Since Last Report)


Item 5. Other Events

      On May 25, 1999, Alexion Pharmaceuticals, Inc. issued the press release
filed herewith as Exhibit 99.

Item 7. Financial Statements, Pro Forma Financial Information and Exhibits.

      (c) Exhibits.

      99    Press Release dated May 25, 1999.


                                   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 hereunto duly authorized.

                                         ALEXION PHARMACEUTICALS, INC.


Date: June 7, 1999             By:              /s/ Leonard Bell
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                                      Name:  Leonard Bell, M.D.
                                      Title: President, Chief Executive Officer,
                                             Secretary and Treasurer


                                                                  
IMMEDIATE RELEASE      Alexion Contacts:      Leonard Bell, M.D.           Lisa Burns, Justin Jackson (Media)
- -----------------                             President and CEO            Burns McClellan 212-213-0006
                                              Alexion Pharmaceuticals      Rhonda Chiger (Investor Relations)
                                              203/776-1790                 Thomson Investor Relations 212-510-9280
Alexion Elects Alvin Parven, Former Head of Operations at Aetna Health Plans to Board of Directors NEW HAVEN, Conn., May 25, 1999 -- Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) today announced that Mr. Alvin S. Parven has been elected to the Company's Board of Directors. A former vice president of operations at Aetna Health Plans, Mr. Parven possesses more than thirty-five years of management experience in the healthcare sector. Mr. Parven, currently President of ASP Associates, a strategic consulting business, previously held several senior management positions at Aetna including Vice President of Pension Services at Aetna, Vice President of Operations at Aetna Health Plans, and Vice President at Aetna Business Consulting. In these capacities, Mr. Parven was responsible for directing the 14,000 employee nationwide healthcare organization and focused on transactions with both the federal government and healthcare providers. During his tenure, Aetna was the largest commercial contractor for Medicare Parts A and B. Mr. Parven also reported directly to the Office of the Chairman and initiated reviews and recommendations concerning the strategic direction of various business units in the corporation. "We are enthused that Al has agreed to join our Board at a time when the Company is preparing to make a transition into late stage clinical development of several promising products. Al's broad operational skills and talents coupled with his specific transaction-oriented experience in healthcare reimbursement, should be valuable assets as the Company continues to build on its development opportunities," said Dr. Leonard Bell, President and Chief Executive Officer of Alexion. Noting that Tim Howe of Collinson, Howe, & Lennox has resigned to commit more time to venture opportunities, Dr. Bell continued, "I would also like to thank Tim Howe for his service over the last several years and wish him continued success." "I am very much looking forward to working with the team of dedicated professionals at Alexion who are systematically focusing on the business of developing new and more effective disease treatments," noted Mr. Parven. "Their commitment to achievement and strategic innovation will be absolutely vital to further building on the company's success to date. I look forward to contributing my skills and understanding of the healthcare market environment to Alexion's strong product development programs." Alexion's two lead product candidates, the C5 inhibitors 5G1.1-SC and 5G1.1, are specific and potent recombinant anti-inflammatory drugs which are designed to selectively intervene in the complement cascade. The Company believes that these proprietary C5 Inhibitors intervene at an optimal point which generally preserves the normal disease-preventing functions of complement proteins while generally inhibiting the disease-causing actions. 5G1.1-SC has been shown to significantly reduce cardiac damage, new cognitive (brain) deficits, and blood loss in Phase I/II and Phase IIa clinical studies in patients undergoing cardiopulmonary bypass (CPB) during coronary artery bypass graft surgery. 5G1.1-SC, currently in a 1000 patient Phase IIb CPB study, is being co-developed with Procter & Gamble Pharmaceuticals for acute cardiovascular indications. 5G1.1, under development for chronic autoimmune indications, has been observed to significantly and beneficially affect objective measurements of disease activity in Phase I/II clinical studies in Rheumatoid Arthritis patients. 5G1.1 has also completed dosing in a Phase I/II clinical study in Systemic Lupus patients. Alexion Pharmaceuticals, Inc. was founded in 1992 and is engaged in the development of selective immunotherapeutic drugs that generally are designed to inhibit the disease-causing segments of the immune system while preserving the disease-preventing aspects of the immune system. The Company is developing three technology platforms: C5 Complement Inhibitors and Apogen T-Cell Therapeutics which together target severe cardiovascular and autoimmune disorders; and xenografts for organ transplantation. This news release contains forward-looking statements. Such statements are subject to certain factors which may cause Alexion's plans to differ or results to vary from those expected including unexpected pre-clinical or clinical results, the need for additional research and testing, delays in manufacturing, access to capital and funding, delays and adverse changes in development of commercial relationships and a variety of 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 1O-K for the year ended July 31, 1998. Alexion undertakes no obligation to publicly release results of any of these forward-looking statements which may be made to reflect events or circumstances after the date hereof or to reflect the occurrence of unanticipated events.