<PAGE>

EXHIBIT 10.31.6  First Amendment to Exchange Agreement, dated May 22, 2003,
                 between Eurotech, Ltd. and Woodward, LLC


                      FIRST AMENDMENT TO EXCHANGE AGREEMENT

         This FIRST AMENDMENT TO EXCHANGE AGREEMENT (this "Amendment"), dated as
of May 22, 2003, is by and among Eurotech, Ltd., a District of Columbia
corporation (the "Company") and Woddward LLC, an entity organized and existing
under the laws of the Cayman Islands ("Woodward"). The Company and Woodward are
collectively referred to herein as the "Parties."

                                    RECITALS

         WHEREAS, the Parties are the parties to that certain Exchange
Agreement, dated March 27, 2003 (the "Exchange Agreement") by and among the
Parties;

         WHEREAS, pursuant to Section 9(f) of the Exchange Agreement, the
Parties must agree in writing to any modification or amendment to the Exchange
Agreement; and

         WHEREAS, the Parties desire to make certain amendments to the Exchange
Agreement in the manner set forth herein.

         NOW, THEREFORE, in consideration of the foregoing premises, and of the
representations, warranties, covenants and agreements contained in the Exchange
Agreement, and for other good and valuable consideration, the receipt and
sufficiency of which is acknowledged by the Parties, the Parties hereby amend
the Exchange Agreement as follows:

         1. DEFINED TERMS. Unless defined herein, all capitalized terms used
herein shall have the meanings ascribed such terms in the Exchange Agreement.

         2. AMENDMENT TO RECITAL A - EXCHANGED STOCK. In order to effect the
understanding and agreement of the Parties as to the accurate number of shares
of Exchanged Stock, Recital A to the Exchange Agreement is hereby deleted in its
entirety and replaced with the following:

         "A. Woodward is the (i) owner of good and marketable title to 25,000
shares of the Eurotech Series A Preferred Stock, and (ii) holder of the right to
have issued to it 11,475 shares of the Eurotech Series B Preferred Stock, in
each case free and clear of all liens and encumbrances (such shares and rights,
the "Exchanged Stock")."

         3. ADDITIONAL AMENDMENTS. The Parties hereby make and agree to all
conforming amendments and modifications to the Exchange Agreement necessary to
reflect amendments to the Exchange Agreement effected by this Amendment.

         4. NO FURTHER AMENDMENT. Except as amended by this Amendment, the
Exchange Agreement shall remain unchanged and in full force and effect.

         5. COUNTERPARTS. This Amendment may be executed in any number of
counterparts, and by facsimile, each such counterpart being deemed to be an
original instrument, and all such counterparts shall together constitute the
same agreement.

<PAGE>

         IN WITNESS WHEREOF, this Amendment has been duly executed and delivered
by the duly authorized officers of the parties hereto as of the date first
written above.


                                        EUROTECH, LTD.


                                        By: /s/ Don V. Hahnfeldt
                                            -------------------------
                                            Name:  Don V. Hahnfeldt
                                            Title: President



                                        WOODWARD LLC


                                        By: /s/ Arlene de Castro  /s/ Ioka Bobb
                                            ------------------------------------
                                            Name: Arlene de Castro and Ioka Bobb
                                            for Navigator Management Ltd.
                                            Title: Director



            [End of Signature Page to Amendment to Exchange Agreement