Document:

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                                                                   EXHIBIT 10.31

                              DECODE GENETICS, INC.

                  SERIES C PREFERRED STOCK REPURCHASE AGREEMENT

     This Series C Preferred Stock Repurchase Agreement ("Agreement") is made
effective as of July 12, 1999 by and between deCODE genetics, Inc., a Delaware
corporation (the "Company"), and Roche Finance Ltd. (the "Seller").

                            PRELIMINARY STATEMENTS

     A.  The Seller is the owner of certain shares of the Company's Series C
Preferred Stock (the "Series C Stock") .

     B.  The Seller wishes to sell to the Company, and the Company wishes to
purchase from the Seller, 100,000 shares of Series C Stock (the "Shares").

     NOW, THEREFORE, the parties hereto, intending to be legally bound, agree as
follows:

     1.   SALE AND PURCHASE OF THE SHARES.

          1.1 Sale and Purchase. Subject to the terms and conditions hereof, the
Seller agrees to sell , and the Company agrees to purchase, the Shares for a
purchase price of Seven Dollars and Fifty Cents ($7.50) per share.

          1.2 Payment for Shares. Following execution and delivery of this
Agreement by the Company and the Seller, the Company shall pay the purchase
price of the Shares by check or wire transfer to such account as the Seller
shall designate.

          1.3 Delivery of Certificates. Upon full payment by the Company of the
purchase price of the Shares, the Seller will deliver to the Company one or more
certificates representing the Shares. In the event that less than all of the
shares represented by a certificate are repurchased, the Company will deliver to
the Seller a new certificate representing the unpurchased shares.
Notwithstanding the foregoing, from and after payment by the Company as provided
in Section 1.2 hereof, all rights of the Seller as a holder of the Shares shall
cease and terminate.

     2.   REPRESENTATIONS OF THE SELLER.

     The Seller hereby represents and warrants to the Company as follows:

          2.1 Power and Authority. It has full power and authority to sell the
Shares and to enter into and perform this Agreement and any other agreements and
instruments to be executed and delivered herewith, and such sale and such
agreements (i) have been duly authorized, (ii) are legal, valid, binding and
enforceable against the Seller and (iii) are not in contravention of any law,
order or agreement by which the Seller is bound.

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          2.2 Title. It has made no prior assignment of the Shares or of any
interest therein. It is the sole legal and beneficial owner of the Shares and
has good and marketable title thereto, free and clear of all liens, claims and
encumbrances of any kind, and will transfer to the Company such good and
marketable title, free and clear of any liens, claims and encumbrances of any
kind.

          2.3 Company Information. It is a sophisticated seller with respect to
the Shares, has adequate information concerning the business and financial
condition of the Company to make an informed decision regarding the sale of the
Shares, and has independently, without reliance upon the Company (other than
reliance upon the representations and warranties of the Company set forth
herein) and based on such information as it deemed appropriate, made its own
analysis and decision to enter into this Agreement, and the Seller acknowledges
and agrees that the Company may possess material information with respect to the
Company not known to the Seller ("Company Information"), that the Seller has not
requested the Company Information and that the Company shall have no liability
to the Seller with respect to the nondisclosure of the Company Information and
the Seller hereby releases the Company therefrom.

     3.   REPRESENTATIONS OF THE COMPANY.

     The Company hereby represents and warrants to the Seller that it has full
power and authority to purchase the Shares and to enter into and perform this
Agreement and any other agreements and instruments to be executed and delivered
herewith, and such purchase and such agreements (i) have been duly authorized,
(ii) are legal, valid, binding and enforceable against the Company and (iii) are
not in contravention of any law, order or agreement by which the Company is
bound.

     4.   MISCELLANEOUS.

          4.1 Governing Law. This Agreement shall be governed by and construed
under the laws of the State of Delaware as applied to agreements among Delaware
residents made and to be performed entirely within the State of Delaware.

          4.2 Binding Effect; Successors and Assigns. Except as otherwise
expressly provided herein, the provisions hereof shall inure to the benefit of,
and be binding upon, the successors, assigns, heirs, executors, and
administrators of the parties hereto.

          4.3 Entire Agreement. This Agreement constitutes the full and entire
understanding and agreement among the parties with regard to the subject matter
hereof.

          4.4 Counterparts. This Agreement may be executed in any number of
counterparts, each of which shall be deemed an original and all of which
together shall constitute one instrument.

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          4.5 Further Action. Each party shall, without further consideration,
take such further action and execute and deliver such further documents as may
be reasonably requested by the other party in order to carry out the provisions
and purposes of this Agreement.

          4.6 Reissuance of Shares. The Company will not sell or otherwise
reissue the Shares without the Seller's written consent.

                                      * * *

This Series C Preferred Stock Repurchase Agreement is hereby executed as of the
date first above written.

                                       deCODE genetics, Inc.

                                       By:    /s/ Kari Stefansson
                                             -----------------------------------
                                              Kari Stefansson, President

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<PAGE>   4

                                       ROCHE FINANCE LTD

                                       By:    /s/ Bruno Maier
                                             -----------------------------------

                                       Name:  Dr. Bruno Maier
                                             -----------------------------------

                                       Title  Director
                                             -----------------------------------

                                       By:    /s/ Peter Matter
                                             -----------------------------------

                                       Name   Peter Matter
                                             -----------------------------------

                                       Title: Director
                                             -----------------------------------

                                       Address:

                                           124 Grenzacherstrasse
                                           CH-4070 Basel
                                           SWITZERLAND
                                           Attention:  CFDV Building 21 Room 292
                                           Facsimile No.:  41-61-688-4169

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<PAGE>   5

                              DECODE GENETICS, INC.

                                   ADDENDUM TO
                  SERIES C PREFERRED STOCK REPURCHASE AGREEMENT

     This Addendum to Series C Preferred Stock Repurchase Agreement (this
"Addendum") is made effective as of March 1, 2000 (the "Effective Date") by and
between deCODE genetics, Inc., a Delaware corporation (the "Company"), and Roche
Finance Ltd. (the "Seller").

                             PRELIMINARY STATEMENTS

     A.   The Company and the Seller entered into a Series C Preferred Stock
Repurchase Agreement, dated July 12, 1999 (the "Series C Repurchase Agreement"),
pursuant to which the Corporation repurchased 100,000 shares (the "Series C
Shares") of the Corporation's Series C Preferred Stock from the Seller at a
closing held on August 24th, 1999 (the "Closing Date").

     B.   It was the understanding among the Company and the Sellers that the
purchase price for the Series C Shares would be equal to the price per share,
net of commissions and other fees payable to the purchaser (the "Purchaser"), at
which the Company sold shares of its Series B Preferred Stock pursuant to a
stock purchase agreement dated as of June 30, 1999 (the "Series B Offering").

     C.   Contemporaneously with the execution of the Series C Repurchase
Agreement, the Company and the Sellers entered into an oral agreement that if
any contingent portion of the purchase price in the Series B Offering became
payable, the purchase price for the Series C Shares would be adjusted upward
accordingly, with the amount of such adjustment to be paid to the Sellers by the
Company after such contingent portion of the purchase price in the Series B
Offering became payable.

     D.   The Company and the Purchaser have entered into an Addendum to Stock
Purchase Agreement confirming that on December 28, 1999, they agreed that a
contingent payment of $7.50, less commissions and other fees payable to the
Purchaser in an amount equal to seven percent (7%) of the sum of the original
purchase price and the contingent payment, was due and payable.

     NOW, THEREFORE, the parties hereto, intending to be legally bound, agree as
follows:

     1.   ADJUSTMENT TO PURCHASE PRICE; PAYMENT OF DEFICIENCY. The adjusted
purchase price for the Series C Shares as of the Closing Date is US$13.95 per
share. Within five business days of the Effective Date, the Company shall pay,
by check or wire transfer to such account as the Seller shall designate, US$6.45
(representing the adjusted purchase price of US$13.95 less the US$7.50 already
paid) for each of the Series C Shares sold to the Company by the Seller under
the Series C Repurchase Agreement.

     2.   RATIFICATION OF AMENDMENT OF AMENDED AND RESTATED INVESTORS' RIGHTS
AGREEMENT. The amendment of the Amended and Restated Investors' Rights Agreement
dated as of February 2, 1998, as amended, among the Company and certain of its
stockholders to grant

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the provisions of Section 2 thereof to the holders of the Series B Preferred
Stock sold in the Series B Offering is hereby ratified, approved and confirmed.

     3.   MISCELLANEOUS. This Addendum shall be governed by and construed under
the laws of the State of Delaware as applied to agreements among Delaware
residents made and to be performed entirely within the State of Delaware. Except
as otherwise expressly provided herein, the provisions hereof shall inure to the
benefit of, and be binding upon, the successors, assigns, heirs, executors, and
administrators of the parties hereto. This Addendum, together with the Series C
Repurchase Agreement, constitutes the full and entire understanding and
agreement among the parties with regard to the subject matter hereof. This
Addendum may be executed in any number of counterparts, each of which shall be
deemed an original and all of which together shall constitute one instrument.
Except as set forth herein, all terms of the Series C Repurchase Agreement
remain unchanged and in full force and effect.

     This Addendum to Series C Preferred Stock Repurchase Agreement is hereby
executed to be effective as of the date first above written.

<PAGE>   7

                                         DECODE GENETICS, INC.

Dated:_______________________            By:  /S/ Kari Stefansson
                                                  Kari Stefansson, President

                                         ROCHE FINANCE LTD

Dated: 29 February 2000                  By:  /s/ Bruno Maier
                                         Name:    Dr. Bruno Maier
                                         Title:   Director

                                         By:      /s/ Beat Krahenmann
                                         Name:    Dr. Beat Krahenmann
                                         Title:   Deputy Director

                                         Address:

                                         124 Grenzacherstrasse
                                         CH-4070 Basel
                                         SWITZERLAND
                                         Attention:  CFDV Building 21 Room 292<PAGE>   1
                                                                   EXHIBIT 10.32

                              DECODE GENETICS, INC.

                        COMMON STOCK REPURCHASE AGREEMENT

         This Common Stock Repurchase Agreement ("Agreement") is made effective
as of July 12, 1999 by and between deCODE genetics, Inc., a Delaware corporation
(the "Company"), and Kari Stefansson (the "Seller").

                             PRELIMINARY STATEMENTS

         A. The Seller is the owner of certain shares of the Company's Common
Stock (the "Common Stock") .

         B. The Seller wishes to sell to the Company, and the Company wishes to
purchase from the Seller, 333,333 shares of Common Stock (the "Shares").

         NOW, THEREFORE, the parties hereto, intending to be legally bound,
agree as follows:

         1.       SALE AND PURCHASE OF  THE SHARES.

                  1.1 Sale and Purchase. Subject to the terms and conditions
hereof, the Seller agrees to sell, and the Company agrees to purchase, the
Shares. The consideration for the Shares shall be 5.625/7.50 of a share of the
Company's Series B Preferred Stock for each Share (for a total of 250,000 shares
of Series B Preferred Stock).

                  1.2 Closing. The closing of the sale and purchase of the
Shares under this Agreement shall be held on July 12, 1999, at the offices of
the Company or at such other time and place as the Company and the Seller may
agree (the "Closing").

                  1.3 Delivery. At the Closing and upon delivery by the Company
of certificates representing the Series B Preferred Stock to be issued in
exchange for the Shares, the Seller will deliver to the Company one or more
certificates representing the Shares. In the event that less than all of the
shares represented by a certificate are repurchased, the Company will deliver to
the Seller a new certificate representing the unpurchased shares.

         2.       REPRESENTATIONS OF THE SELLER.

         The Seller hereby represents and warrants to the Company as follows:

                  2.1 Power and Authority. He has full power and authority to
sell the Shares and to enter into and perform this Agreement and any other
agreements and instruments to be executed and delivered herewith, and such sale
and such agreements (i) have been duly authorized, (ii) are legal, valid,
binding and enforceable against him and (iii) are not in contravention of any
law, order or agreement by which he is bound.

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<PAGE>   2
                  2.2 Title He has made no prior assignment of the Shares or of
any interest therein. He is the sole legal and beneficial owner of the Shares
and has good and marketable title thereto, free and clear of all liens, claims
and encumbrances of any kind, and will transfer to the Company such good and
marketable title, free and clear of any liens, claims and encumbrances of any
kind.

                  2.3 Company Information. He is a sophisticated seller with
respect to the Shares, has adequate information concerning the business and
financial condition of the Company to make an informed decision regarding the
sale of the Shares, and has independently, without reliance upon the Company
(other than reliance upon the representations and warranties of the Company set
forth herein) and based on such information as he deemed appropriate, made his
own analysis and decision to enter into this Agreement, and he acknowledges and
agrees that the Company may possess material information with respect to the
Company not known to him ("Company Information"), that he has not requested the
Company Information and that the Company shall have no liability to him with
respect to the nondisclosure of the Company Information and he hereby releases
the Company therefrom.

         3.       REPRESENTATIONS OF THE COMPANY.

         The Company hereby represents and warrants to the Seller that it has
full power and authority to purchase the Shares and to enter into and perform
this Agreement and any other agreements and instruments to be executed and
delivered herewith, and such purchase and such agreements (i) have been duly
authorized, (ii) are legal, valid, binding and enforceable against the Company
and (iii) are not in contravention of any law, order or agreement by which the
Company is bound.

         4.       MISCELLANEOUS.

                  4.1 Governing Law. This Agreement shall be governed by and
construed under the laws of the State of Delaware as applied to agreements among
Delaware residents made and to be performed entirely within the State of
Delaware.

                  4.2 Successors and Assigns. Except as otherwise expressly
provided herein, the provisions hereof shall inure to the benefit of, and be
binding upon, the successors, assigns, heirs, executors, and administrators of
the parties hereto.

                  4.3 Entire Agreement. This Agreement constitutes the full and
entire understanding and agreement among the parties with regard to the subject
matter hereof.

                  4.4 Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall be deemed an original and all of which
together shall constitute one instrument.

                                       2
<PAGE>   3

         4.5 Further Action. Each party shall, without further consideration,
take such further action and execute and deliver such further documents as may
be reasonably requested by any other party in order to carry out the provisions
and purposes of this Agreement.

                                      * * *

This Common Stock Repurchase Agreement is hereby executed as of the date first
above written.

                                   deCODE genetics, Inc.

                                   By:   /s/ Hannes Smarason
                                         ----------------------------------
                                         Hannes Smarason, Senior Vice President
                                         & Chief Financial Officer

                                         /s/ Kari Stefansson
                                         -----------------------------------
                                         Kari Stefansson

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