INDEFINITE TERM EMPLOYMENT AGREEMENT

EXHIBIT 10.1

English Translation

INDEFINITE TERM

EMPLOYMENT AGREEMENT

BETWEEN THE UNDERSIGNED:

Alexion Europe SAS, a société par actions simplifiée, with a capital of EUR 37,000 registered with the Paris Registry of Commerce and Companies under the number B ###-###-####, whose registered office is located at 54/56 avenue Hoche – Paris (75008), represented for the purposes hereof by Mr. David Keiser, in his capacity as President

hereinafter known as the “Company”

on the one hand,

AND:

Mr. Patrice Coissac, born on October 5, 1948, of French nationality, residing at 6, Square Alboni, 75016 Paris

hereinafter known as “Mr. Coissac”

on the other hand,

The Company and Mr. Coissac being collectively referred to hereinafter as the “Parties”.

IT HAS BEEN AGREED AS FOLLOWS:

ARTICLE 1: ENGAGEMENT

Mr. Coissac is hired by the Company for an indefinite term, as from the date of signature of this Employment Agreement indicated at the end hereof (the “Signature Date”), as Operations Manager Europe subject to the results of a pre-hiring medical examination.

It is expressly agreed that Mr. Coissac’s engagement is subordinated to the condition that he is fully free from any other work relationship or obligation to another employer and in particular, from any non-competition obligation relating to the Company’s activity.

ARTICLE 2: DUTIES

Mr. Coissac is engaged as Operations Manager Europe, in charge of Marketing, Sales and Distribution, Group XI of the applicable Collective Bargaining Agreement, with Executive status.

As Operations Manager Europe, Mr. Coissac will, consistent with the nature of the activity of the company:

The parties agree that the list of duties mentioned above is not exhaustive, as the Company reserves the right to modify the duties, insofar as such modifications are compatible with Mr. Coissac’s experience and skills, without such modifications being considered as modifications of his employment agreement, which is expressly acknowledged by Mr. Coissac by the signature hereof.

Mr. Coissac will report to the President of Alexion Pharmaceuticals, Inc. on a timely basis and as determined by the Company and Alexion Pharmaceuticals, Inc.

ARTICLE 3: TRIAL PERIOD

The trial period is fixed at three (3) months of effective work as from the date of engagement.

During this period, each of the parties may terminate this Employment Agreement at any time, without indemnities or notice period.

ARTICLE 4: WORK PLACE

For the record, Mr. Coissac shall be based in the premises of the Company, currently located at 54/56 avenue Hoche in Paris (75008).

Mr. Coissac acknowledges that his place of work could be transferred to any other place in metropolitan France or Brussels, Belgium, if the Company so requires. Mr. Coissac expressly acknowledges by the signature hereof, that any such transfer shall not be considered as a modification of his employment agreement. In the event of such a transfer, the Company and Mr. Coissac will agree on an appropriate adjustment to keep Mr. Coissac economically whole for the period of such transfer, in particular from a personal income tax and social charges standpoint. Any proposed transfer of Mr. Coissac to another location than metropolitan France or Brussels, Belgium will be the subject of a separate negotiation between the Parties.

Moreover, due to the nature of his duties, which implies a high level of mobility, and in view of the nature of the Company’s activity, Mr. Coissac shall be required to make regular business trips, both in France and abroad (including Europe, USA, Asia), which he hereby expressly accepts.

ARTICLE 5: REMUNERATION

In consideration for the performance of his duties, Mr. Coissac shall receive an annual basic lump sum gross salary of EUR 170,000 (one hundred and seventy thousand Euros), payable in twelve (12) monthly installments.

Mr. Coissac shall also benefit from an individual incentive scheme as from the Company’s 2005/2006 fiscal year, subject to meeting the targets which shall be fixed at a later date and which shall be specified in an amendment to the present Employment Agreement. Such bonus may equal (i) for the fiscal year 2005-2006, a maximum of EUR 110,000 (one hundred ten thousand Euros) and (ii) for each subsequent year, a maximum of 50% of Mr. Coissac’s annual base salary (based upon a full 12 months of service) plus his total expatriation premium paid during such year as provided below, in the case of both (i) and (ii) as may be determined by the CEO and President of Alexion Pharmaceuticals, Inc. based on achievement of objectives calculated at the level of Alexion Pharmaceuticals, Inc. and agreed to individual goals.

The annual incentive scheme includes the indemnity for legal paid holidays.

In consideration for the amount of travel which Mr. Coissac will be called upon to undertake in the course of his professional duties, the Company shall also pay to Mr. Coissac an expatriation premium, calculated as provided in Appendix I hereto.

The Company will also pay Mr. Coissac a signing bonus equal to EUR 20,000 gross (twenty thousand Euros) payable in two installments of EUR 10,000 (ten thousand Euros) on the Signature Date and April 1, 2006.

Mr. Coissac’s remuneration will be re-evaluated on an annual basis and adjusted at the end of the fiscal year (July 31). The first such re-evaluation and adjustment shall be effective on August 1, 2006.

ARTICLE 6: WORKING TIME

In view of his level of remuneration, the nature of his duties and the actual conditions of their performance, which necessitate a large amount of self sufficiency in the organization of his work schedule and enable him to have vast autonomy in decision making, it has been agreed that his gross salary is an all-inclusive compensation for his activities and is not related to the number of working hours that Mr. Coissac shall actually have to carry out in order to complete his duties, since he has senior executive status.

ARTICLE 7: PAID VACATION

Mr. Coissac’s rights to paid vacation shall be determined in accordance with the applicable legal and collective bargaining agreement provisions.

The dates of vacation absence of Mr. Coissac shall be determined by mutual agreement between Mr. Coissac and the Company according to the needs of the activity of the Company.

ARTICLE 8: BUSINESS EXPENSES

The Company shall reimburse Mr. Coissac for any reasonable expenses incurred in the performance of his duties, upon presentation of appropriate receipts, in accordance with the Company’s policy in force which may be modified at any time, and of which Mr. Coissac agrees he has been informed.

For the purposes of the foregoing, business class air travel by Mr. Coissac shall be considered reasonable.

ARTICLE 9: CAR ALLOWANCE

Mr. Coissac will be entitled to a car allowance in an approximate amount of EUR 1,000 (one thousand euros) gross per month, all as shall be determined by a separate agreement between Alexion and Mr. Coissac.

ARTICLE 10: SOCIAL COVERAGE

With regard to the application of laws on social security and pension and death and disability schemes, the Parties agree to reciprocally comply with all statutory or contractual provisions, current or future, governing these matters.

Mr. Coissac shall benefit from all the complementary pension and death and disability regimes in force within the Company or that are put into effect in the future, for employees of the same category.

In this respect, Mr. Coissac shall contribute to these regimes by having his contributions deducted from his salary.

ARTICLE 11: ABSENCES, ILLNESS

Any foreseeable absence must be authorized by the Company.

Moreover, in the event of illness or a force majeure event, Mr. Coissac shall inform the Company as soon as possible, so that every useful measure may be taken to ensure that the activity is carried out. Mr. Coissac shall provide the appropriate justifications within a maximum period of forty eight (48) hours.

ARTICLE 12: INVENTIONS

Any inventions and improvements to inventions, designs or development of software, literary or artistic creations, whether protectible or not, made by Mr. Coissac or to which he might have contributed during or at the time of his employment or the performance of his duties and any industrial property rights and related authors’ rights (droits d’auteur) shall be and shall remain the exclusive property of the Company and shall be governed by the provisions of the Collective Bargaining Agreement. At the first demand of the Company, Mr. Coissac undertakes to sign any documents and perform all formalities that may be necessary for the Company to obtain a patent or any other intellectual property protection relating to inventions, software, literary and artistic creations, discoveries and their improvements.

ARTICLE 13: PROFESSIONAL OBLIGATIONS

Mr. Coissac undertakes, both during the performance of this Employment Agreement and in particular, after its possible termination, for any reason whatsoever, to keep absolutely confidential all the information of which he has knowledge or acquired during the performance of his duties, and not to disclose the identity of the suppliers, clients or partners of the Company to third parties.

Mr. Coissac undertakes not to disclose to any third parties both during the duration of his Agreement with Company and after its possible termination, any of the projects, studies and creations made on behalf of the Company or the companies of the Group or on behalf of the clients of the Company or the Group.

During the entire term of this Employment Agreement, Mr. Coissac shall devote the exclusivity of his services to the Company and cannot have any other professional obligation, even if this activity is not competitive with that of the Company, without the prior written agreement of the Company, subject to the following exception: it has been agreed between the Parties that Mr. Coissac would remain Gérant and shareholder of BioPharmaConsult provided that (i) Mr. Coissac shall not perform any operational duties at BioPharmaConsult and (ii) his position as Gérant or shareholder of such Company shall not be competitive with that of the Company and shall not interfere in any way with the performance of his duties pursuant to this Agreement.

ARTICLE 14: PROHIBITION OF ENTICEMENT

Mr. Coissac may not directly or through a third party without the prior written consent of the Company for a period of one year after the end of this Employment Agreement, whatever the reason for the termination, offer any enticement to, solicit or hire - in whatever manner and in whatever title or capacity - any individual who was during the one year period prior to the termination of this contract employed by the Company or during the three month period prior to the termination of this contract was involved in discussions with a view to being employed by the Company and to whom the Company makes a written offer at the latest 3 months following such termination.

ARTICLE 15: RESTITUTION

Mr. Coissac expressly undertakes to return or transfer, on the same day as the termination of his duties within the Company, for any reason whatsoever and without the Company having to take any steps or give formal notice, all the documents, supports containing information and data, equipment or objects in his possession relating to the Company, the companies of the Group or any client, suppliers or third parties, which he may have obtained in any capacity whatsoever, in the context of his activity within the Company.

Mr. Coissac undertakes, pursuant to the same terms, to return any equipment which would have been entrusted to him for carrying out his duties.

ARTICLE 16: TERMINATION OF AGREEMENT

As this Agreement is concluded for an indefinite term, either Party may terminate it at the end of the notice period, in accordance with the applicable law and the Collective Bargaining Agreement, provided that prior notice of three (3) months is given, except that, no notice period is required in the case of gross or willful misconduct or a force majeure event.

ARTICLE 17: APPLICABLE LAW

This Agreement shall be governed by French law. For anything not set forth herein, the Parties shall refer to the legal provisions in force as well as the provisions of the applicable collective bargaining agreement in force at the Company, which, at the date of this agreement and for information, is the National Collective Bargaining Agreement for Pharmaceutical Industries.

Executed in Paris, France,

On November 7, 2005 (the “Signature Date”)

In two originals, including one for each of the Parties.

The signatures of the Parties shall be preceded by the handwritten words “Read and approved”.

APPENDIX I

Expatriation Premium

pursuant to article 81 A III of the General Tax Code

(i) Mr. Coissac will receive, in addition to his base salary, 300 Euros (three hundred Euros) gross per day of presence in a foreign country, if such foreign country is located in Europe.

(ii) Mr. Coissac will be entitled to 600 Euros (six hundred Euros) gross per day spent outside Europe.

(iii) The day of departure and the day of arrival will each count for a full day.

Saturdays and Sundays spent abroad for the Company will each also count for one day.

(iv) One day will be added if Mr. Coissac stays abroad five days on end without being in a position to revisit his home.

(v) The total amount of the indemnity as computed above will be multiplied by two (2) if Mr. Coissac has stayed more than 45 days abroad in a given fiscal year of the Company.

The signatures of the Parties shall be preceded by the handwritten words “Read and approved”.