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                                                                     EXHIBIT 4.2

                           INVESTORS' RIGHTS AGREEMENT


     This Investors' Rights Agreement (the "AGREEMENT") is made as of July 24,
2000 by and among Third Wave Technologies, Inc., a Wisconsin corporation (the
"COMPANY") and the persons and entities listed on Schedule A attached hereto.

     WHEREAS, the Company previously sold and issued 7,223 shares of its
Preferred Stock, 943 shares of which are designated Series A Preferred Stock,
500 shares of which are designated Series B Preferred Stock, 467 shares of which
are designated Series C Preferred Stock, 988 shares of which are designated
Series D Preferred Stock, and 4,325 shares of which are designated Series E
Preferred Stock, to those persons and entities set forth on Exhibit 1 hereto
(collectively, the "Existing Preferred Stockholders");

     WHEREAS, simultaneously herewith, the Company is entering into a Series F
Preferred Stock Purchase Agreement (the "Series F Agreement") and issuing shares
of its Series F Preferred Stock to the Investors named in Exhibit A to the
Series F Agreement (collectively the "Series F Stockholders").

     NOW, THEREFORE, it is hereby agreed as follows:

     1.   Certain Definitions. As used in this Agreement, the following terms
shall have the following respective meanings:

     "COMMISSION" shall mean the Securities and Exchange Commission or any other
federal agency at the time administering the Securities Act.

     "CONVERSION STOCK" shall mean the shares of Common Stock issued or issuable
upon conversion of the Shares.

     "HOLDER" shall mean the holders of Registrable Securities, securities
convertible into Registrable Securities and any person holding such securities
to whom the rights under this Agreement have been transferred in accordance with
Section 3.13 hereof.

     "PURCHASERS" shall mean: (i) the purchasers of the Company's previously
issued Series A Preferred Stock, Series B Preferred Stock, Series C Preferred
Stock, Series D Preferred Stock, and Series E Preferred Stock pursuant to the
applicable Investment Agreement and (ii) the purchasers of the Company's Series
F Preferred Stock to be issued pursuant to the Series F Agreement.

     "REGISTRABLE SECURITIES" means (i) the Conversion Stock and (ii) any Common
Stock of the Company issued or issuable with respect to, or in exchange for or
in replacement of the Conversion Stock or other securities convertible into or
exercisable for Conversion Stock upon any stock split, stock dividend,
recapitalization, or similar event, provided, however, that shares of Common
Stock shall only be treated as Registrable Securities if and so long as they
have not been sold to or through a broker or dealer or underwriter in a public
distribution or a public securities transaction.

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     The terms "REGISTER," "REGISTERED" and "REGISTRATION" refer to a
registration effected by preparing and filing a registration statement in
compliance with the Securities Act, and the declaration or ordering of the
effectiveness of such registration statement.

     "REGISTRATION EXPENSES" shall mean all expenses, except Selling Expense
(defined below), incurred by the Company in complying with Sections 3.5, 3.6 and
3.7 hereof, including, without limitation, all registration, qualification and
filing fees, printing expenses, escrow fees, fees and disbursements of counsel
for the Company, blue sky fees and expenses, the expense of any special audits
incident to or required by any such registration (but excluding the compensation
of regular employees of the Company which shall be paid in any event by the
Company).

     "RESTRICTED SECURITIES" shall mean the securities of the Company required
to bear the legend set forth in Section 3.2 hereof.

     "SECURITIES ACT" shall mean the Securities Act of 1933, as amended, or any
similar federal statute and the rules and regulations of the Commission
thereunder, all as the same shall be in effect at the time.

     "SELLING EXPENSES" shall mean all underwriting discounts, selling
commissions, fees and disbursements of counsel to the selling Holders and stock
transfer taxes applicable to the securities registered by the Holders.

     "SHARES" shall mean: (i) the shares of the Company's previously issued
Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock,
Series D Preferred Stock, and Series E Preferred Stock, pursuant to the
applicable Investment Agreement and (ii) the shares of the Company's Series F
Preferred Stock to be issued pursuant to the Series F Agreement.

     2.   Prior Agreements. The parties hereto agree that this Agreement shall
supersede and cancel and, where applicable, serve as a valid waiver and consent
as required to amend, supersede or cancel, any prior agreement made between the
Company and any of the Existing Preferred Stockholders or Series F Stockholders
to the extent that any such prior agreement refers to the registration, right of
first refusal, preemptive right, information or reporting right, conversion, or
transfer (including restrictions thereon) of or in connection with any security
of the Company, except in the case of the Series F Agreement and such prior
agreements executed in connection therewith.

     3.   Restrictions on Transfer of Securities; Compliance with Securities
Act; Registration Rights.

          3.1  Restrictions on Transfer. The Shares and the Conversion Stock
shall not be sold, assigned, transferred or pledged except upon the conditions
specified in this Section 3, which conditions are intended to ensure compliance
with the provisions of the Securities Act. The Purchasers will cause any
proposed purchaser, assignee, transferee, or pledgee of the Shares or the
Conversion Stock held by the Purchasers to agree to take and hold such
securities subject to the provisions and upon the conditions specified in this
Section 3.

          3.2  Restrictive Legend. Each certificate representing (i) the Shares,
(ii) the Conversion Stock or (iii) any other securities issued in respect of the
Shares or the Conversion Stock


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upon any stock split, stock dividend, recapitalization, merger, consolidation or
similar event, shall (unless otherwise permitted by the provisions of Section
3.3 below) be stamped or otherwise imprinted with a legend in the following form
(in addition to any legend required under applicable state securities laws):

          THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE BEEN
          ACQUIRED FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER
          THE SECURITIES ACT OF 1933, AS AMENDED. SUCH SHARES MAY NOT
          BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION
          UNLESS THE COMPANY RECEIVES AN OPINION OF COUNSEL REASONABLY
          ACCEPTABLE TO IT STATING THAT SUCH SALE OR TRANSFER IS
          EXEMPT FROM THE REGISTRATION AND PROSPECTUS DELIVERY
          REQUIREMENTS OF SAID ACT. COPIES OF THE AGREEMENT COVERING
          THE PURCHASE OF THESE SHARES AND RESTRICTING THEIR TRANSFER
          MAY BE OBTAINED AT NO COST BY WRITTEN REQUEST MADE BY THE
          HOLDER OF RECORD OF THIS CERTIFICATE TO THE SECRETARY OF THE
          CORPORATION AT THE PRINCIPAL EXECUTIVE OFFICES OF THE
          CORPORATION.

     The Purchasers and Holders consent to the Company making a notation on its
records and giving instructions to any transfer agent of the Shares or the
Conversion Stock in order to implement the restrictions on transfer established
in this Section 3.

          3.3  Notice of Proposed Transfers. The holder of each certificate
representing Restricted Securities by acceptance thereof agrees to comply in all
respects with the provisions of this Section 3.3. Prior to any proposed sale,
assignment, transfer or pledge of any Restricted Securities (other than (i) a
transfer not involving a change in beneficial ownership, including, without
limitation a transfer to a successor trustee, (ii) transactions involving the
distribution without consideration of Restricted Securities by any Holder to any
of its members, partners, or retired partners or members, or to the estate of
any of its members, partners or retired partners or members, (iii) a transfer to
an affiliated fund, partnership or company, or other entity under common
management and control, which is not a competitor of the Company, subject to
compliance with applicable securities laws, or (iv) transfers in compliance with
Rule 144(k), so long as the Company is furnished with satisfactory evidence of
compliance with such Rule), unless there is in effect a registration statement
under the Securities Act covering the proposed transfer, the holder thereof
shall give written notice to the Company of such holder's intention to effect
such transfer, sale, assignment or pledge. Each such notice shall describe the
manner and circumstances of the proposed transfer, sale, assignment or pledge in
sufficient detail, and, if requested by the Company, shall be accompanied, at
such holder's expense, by either (i) a written opinion of legal counsel who
shall, and whose legal opinion shall be, reasonably satisfactory to the Company
addressed to the Company, to the effect that the proposed transfer of the
Restricted Securities may be effected without registration under the Securities
Act, or (ii) a "no action" letter from the Commission to the effect that the
transfer of such securities without registration will not result in a
recommendation by the staff of the Commission that action be taken with respect
thereto, whereupon the holder of such


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Restricted Securities shall be entitled to transfer such Restricted Securities
in accordance with the terms of the notice delivered by the holder to the
Company. Each certificate evidencing the Restricted Securities transferred as
above provided shall bear, the appropriate restrictive legend set forth in
Section 3.2 above, except that such certificate shall not bear such restrictive
legend if in the opinion of counsel for such holder and in the reasonable
opinion of the Company such legend is not required in order to establish
compliance with any provision of the Securities Act.

          3.4  Removal of Restrictions on Transfer of Securities. Any legend
referred to in Section 3.2 hereof stamped on a certificate evidencing the
Restricted Securities and the stock transfer instructions and record notations
with respect to such Restricted Security shall be removed and the Company shall
issue a certificate without such legend to the holder of such Restricted
Security if such security is registered under the Securities Act, or if such
holder provides the Company with an opinion of counsel (which may be counsel for
the Company) reasonably acceptable to the Company to the effect that a public
sale or transfer of such security may be made without registration under the
Securities Act or such holder provides the Company with reasonable assurances,
which may, at the option of the Company, include an opinion of counsel
satisfactory to the Company, that such security can be sold pursuant to Section
(k) of Rule 144 under the Securities Act.

          3.5  Requested Registration.

               (a)  Request for Registration. If the Company shall receive, at
any time after the earlier of (i) July 24, 2004 or (ii) the date six (6) months
after the effective date of the Company's first registered public offering of
its stock, a written request from the Holders of at least a majority of the
Registrable Securities that the Company effect any registration, qualification
or compliance with respect to at least twenty percent (20%) of the Registrable
Securities, or any lesser number of shares of Registrable Securities if the
anticipated aggregate offering price exceeds $10,000,000, the Company will:

                    (i)  within ten days of the receipt by the Company of such
notice, give written notice of the proposed registration, qualification or
compliance to all other Holders; and

                    (ii) as soon as practicable, use its best efforts to effect
such registration, qualification or compliance (including, without limitation,
appropriate qualification under applicable blue sky or other state securities
laws and appropriate compliance with applicable regulations issued under the
Securities Act and any other governmental requirements or regulations) as may be
so requested and as would permit or facilitate the sale and distribution of all
or such portion of such Registrable Securities as are specified in such request,
together with all or such portion of the Registrable Securities of any Holder or
Holders joining in such request as are specified in a written request received
by the Company within 20 days after receipt of such written notice from the
Company.

     Notwithstanding the foregoing, the Company shall not be obligated to take
any action to effect any such registration, qualification or compliance pursuant
to this Section 3.5:


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                         (A)  In any particular jurisdiction in which the
Company would be required to qualify as a foreign corporation, subject itself to
taxation in that jurisdiction or execute a general consent to service of process
in effecting such registration, qualification or compliance unless the Company
is already subject to service in such jurisdiction and except as may be required
by the Securities Act;

                         (B)  During the period starting with the date sixty
(60) days prior to the Company's estimated date of filing of, and ending on the
date six (6) months immediately following the effective date of, any
registration statement pertaining to securities of the Company (other than a
registration of securities in a Rule 145 transaction, with respect to an
employee benefit plan or with respect to the Company's first registered public
offering of its stock), provided that the Company is actively employing in good
faith all reasonable efforts to cause such registration statement to become
effective;

                         (C)  After the Company has effected one such
registration pursuant to this Section 3.5(a) covering all shares requested to be
registered by the Holders initiating or joining such request, and such
registrations have been declared or ordered effective; or

                         (D)  If the Company shall furnish to such Holders a
certificate signed by the President of the Company stating that in the good
faith judgment of the Board of Directors it would be seriously detrimental to
the Company or its shareholders for a registration statement to be filed in the
near future, then the Company's obligation to use its best efforts to register,
qualify or comply under this Section 3.5 shall be deferred for a period not to
exceed 90 days from the date of receipt of written request from the Holders;
provided, however, that the Company shall not exercise such right more than once
in any twelve-month period.

     Subject to the foregoing clauses (A) through (D), the Company shall file a
registration statement covering the Registrable Securities so requested to be
registered as soon as practicable, after receipt of the request or requests of
the Holders.

               (b)  Underwriting. In the event that a registration pursuant to
Section 3.5 is for a registered public offering involving an underwriting, the
Company shall so advise the Holders as part of the notice given pursuant to
Section 3.5(a)(i). In such event, the right of any Holder to registration
pursuant to Section 3.5 shall be conditioned upon such Holder's participation in
the underwriting arrangements required by this Section 3.5, and the inclusion of
such Holder's Registrable Securities in the underwriting to the extent requested
shall be limited to the extent provided herein.

     The Company shall (together with all Holders proposing to distribute their
securities through such underwriting) enter into an underwriting agreement in
customary form with the managing underwriter of recognized national standing
selected for such underwriting by the Company. Notwithstanding any other
provision of this Section 3.5, if the managing underwriter determines that
marketing factors require a limitation of the number of shares to be
underwritten, the managing underwriter may limit the Registrable Securities and
other securities to be distributed through such underwriting. The Company shall
so advise all Holders distributing their securities through such underwriting of
such limitation and the number of shares of Registrable Securities that


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may be included in the registration (and underwriting if any) shall be allocated
among all Holders in proportion, as nearly as practicable, to the respective
amounts of Registrable Securities requested by such Holders to be included in
such Registration Statement. No Registrable Securities excluded from the
underwriting by reason of the underwriter's marketing limitation shall be
included in such registration. To facilitate the allocation of shares in
accordance with the above provisions, the Company may round the number of shares
allocated to any Holder or Holders to the nearest 100 shares.

     If any Holder of Registrable Securities disapproves of the terms of the
underwriting, such Holder may elect to withdraw therefrom by written notice to
the Company, the managing underwriter and the Holders. The Registrable
Securities and/or other securities so withdrawn shall also be withdrawn from
registration, and such Registrable Securities shall not be transferred in a
public distribution prior to 180 days after the effective date of such
registration, or such other shorter period of time as the underwriters may
require.

          3.6  Company Registration.

               (a)  Notice of Registration. If at any time or from time to time
following the Company's initial public offering of securities, the Company shall
determine to register any of its securities, either for its own account or the
account of a security holder or holders, other than (i) a registration relating
solely to employee benefit plans, (ii) a registration relating solely to a Rule
145 transaction, or (iii) a registration pursuant to Section 3.5 hereof, the
Company will:

                    (i)  promptly give to each Holder written notice thereof;
and

                    (ii) include in such registration (and any related
qualification under blue sky laws or other compliance), and in any underwriting
involved therein, all the Registrable Securities specified in a written request
or requests, made within 20 days after receipt of such written notice from the
Company, by any Holder.

               (b)  Underwriting. If the registration of which the Company gives
notice is for a registered public offering involving an underwriting, the
Company shall so advise the Holders as a part of the written notice given
pursuant to Section 3.6(a)(i). In such event the right of any Holder to
registration pursuant to Section 3.6 shall be conditioned upon such Holder's
participation in such underwriting and the inclusion of Registrable Securities
in the underwriting to the extent provided herein.

     All Holders proposing to distribute their securities through such
underwriting shall (together with the Company) enter into an underwriting
agreement in customary form with the managing underwriter selected for such
underwriting by the Company. Notwithstanding any other provision of this Section
3.6, if the managing underwriter determines that marketing factors require a
limitation of the number of shares to be underwritten, the managing underwriter
may limit or exclude the Registrable Securities and other securities to be
distributed through such underwriting. The Company shall so advise all Holders
distributing their securities through such underwriting of such limitation and
the number of shares of Registrable Securities that may be included in the
registration (and underwriting if any) shall be allocated among all Holders in
proportion, as nearly as


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practicable, to the respective amounts of Registrable Securities requested by
such Holders to be included in such Registration Statement. No Registrable
Securities excluded from the underwriting by reason of the underwriter's
marketing limitation shall be included in such registration. To facilitate the
allocation of shares in accordance with the above provisions, the Company may
round the number of shares allocated to any Holder or Holders to the nearest 100
shares. In no event shall the number of Registrable Shares underwritten in an
offering be limited unless and until all shares held by persons other than the
holders of the Registrable Shares and the Company are completely excluded from
such offering.

     If any Holder or Holders disapprove of the terms of any such underwriting,
such Holder or Holders may elect to withdraw therefrom by written notice to the
Company and the managing underwriter. Any securities excluded or withdrawn from
such underwriting shall be withdrawn from such registration, and shall not be
transferred in a public distribution prior to 180 days after the effective date
of the registration statement relating thereto, or such other shorter period of
time as the underwriters may require.

          (c)  Right to Terminate Registration. The Company shall have the right
to terminate or withdraw any registration initiated by it under this Section 3.6
prior to the effectiveness of such registration whether or not any Holder has
elected to include securities in such registration. The Registration Expenses of
such withdrawn registration shall be borne by the Company in accordance with
Section 3.8 hereof.

          3.7  Registration on Form S-3.

          (a)  If any Holder or Holders request in writing that the Company file
a registration statement on Form S-3 (or any successor form to Form S-3), or any
similar short-form registration statement, for a public offering of Registrable
Securities, the reasonably anticipated aggregate price to the public of which,
net of underwriting discounts and commissions (if any), would exceed $1,000,000
and the Company is a registrant entitled to use Form S-3 to register the
Registrable Securities for such an offering, the Company shall use its best
efforts to cause such Registrable Securities to be registered on such form for
the offering and to cause such Registrable Securities to be qualified in such
jurisdictions as the Holder or Holders may reasonably request; provided,
however, that the Company shall not be required to effect more than one such
registration in any twelve (12) month period. The provisions of Section 3.6(b)
shall be applicable to each registration initiated under this Section 3.7.

          (b)  Notwithstanding the foregoing, the Company shall not be obligated
to take any action pursuant to this Section 3.7: (i) in any particular
jurisdiction in which the Company would be required to execute a general consent
to service of process in effecting such registration, qualification or
compliance unless the Company is already subject to service in such jurisdiction
and except as may be required by the Securities Act; (ii) if the Company, within
ten (10) days of the receipt of the request of the initiating Holders, gives
notice of its bona fide intention to effect the filing of a registration
statement with the Commission within ninety (90) days of receipt of such request
(other than with respect to a registration statement relating to a Rule 145
transaction, or an offering solely to employees); (iii) during the period
starting with the date sixty (60) days prior to the Company's estimated date of
filing of, and ending on the date six (6) months immediately following,


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<PAGE>   8

the effective date of any registration statement pertaining to securities of the
Company (other than a registration of securities in a Rule 145 transaction or
with respect to an employee benefit plan), provided that the Company is actively
employing in good faith all reasonable efforts to cause such registration
statement to become effective; or (iv) if the Company shall furnish to such
Holder a certificate signed by the President of the Company stating that in the
good faith judgment of the Board of Directors it would be seriously detrimental
to the Company or its shareholders for registration statements to be filed in
the near future, then the Company's obligation to use its best efforts to file a
registration statement shall be deferred for a period not to exceed 90 days from
the receipt of the request to file such registration by such Holder; provided,
however, that the Company shall not exercise such right more than once in any
twelve-month period.

          3.8  Expenses of Registration. All Registration Expenses incurred in
connection with registrations pursuant to Sections 3.5, 3.6 and 3.7 shall be
borne by the Company. All Selling Expenses relating to securities registered on
behalf of the Holders shall be borne by each holder of securities included in
such registration, to the extent incurred by such holder; provided, however,
that the Company shall not be required to pay for any expenses of any
registration proceeding begun pursuant to Section 3.5 if the registration
request is subsequently withdrawn at the request of the Holders of a majority of
the Registrable Securities to be registered (in which case all participating
Holders shall bear such expenses); provided further, however, that if at the
time of such withdrawal, the Holders have learned of a material adverse change
in the condition, business, or prospects of the Company which did not exist at
the time of their request, then the Holders shall not be required to pay any of
such expenses.

          3.9  Registration Procedures. In the case of each registration,
qualification or compliance effected by the Company pursuant to this Section 3,
the Company will keep each Holder advised in writing as to the initiation of
each registration, qualification and compliance and as to the completion
thereof. At its expense the Company will:

               (a)  Prepare and file with the Commission a registration
statement with respect to such securities and use its best efforts to cause such
registration statement to become and remain effective for thirty (30) days or
less if the distribution described in the Registration Statement has been
completed;

               (b)  Prepare and file with the Commission such amendments and
supplements to such registration statement and the prospectus used in connection
with such registration statement as may be necessary to comply with the
provisions of the Securities Act with respect to the disposition of all
securities covered by such registration statement.

               (c)  Furnish to the Holders participating in such registration
and to the underwriters of the securities being registered such reasonable
number of copies of the registration statement, preliminary prospectus, final
prospectus and such other documents as such underwriters may reasonably request
in order to facilitate the public offering of such securities.

               (d)  Use its best efforts to register and qualify the securities
covered by such registration statement under such other securities or Blue Sky
laws of such jurisdictions as shall be reasonably requested by the Holders,
provided that the Company shall not be required in


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<PAGE>   9

connection therewith or as a condition thereto to qualify to do business or to
file a general consent to service of process in any such states or
jurisdictions.

               (e)  In the event of any underwritten public offering, enter into
and perform its obligations under an underwriting agreement, in usual and
customary form, with the managing underwriter(s) of such offering. Each Holder
participating in such underwriting shall also enter into and perform its
obligations under such an agreement.

               (f)  Notify each Holder of Registrable Securities covered by such
registration statement at any time when a prospectus relating thereto is
required to be delivered under the Securities Act of the happening of any event
as a result of which the prospectus included in such registration statement, as
then in effect, includes an untrue statement of a material fact or omits to
state a material fact required to be stated therein or necessary to make the
statements therein not misleading in the light of the circumstances then
existing.

               (g)  Furnish, at the request of a majority of the Holders
participating in the registration, on the date that such Registrable Securities
are delivered to the underwriters for sale, if such securities are being sold
through underwriters, or, if such securities are not being sold through
underwriters, on the date that the registration statement with respect to such
securities becomes effective, (i) an opinion, dated as of such date, of the
counsel representing the Company for the purposes of such registration, in form
and substance as is customarily given to underwriters in an underwritten public
offering and reasonably satisfactory to a majority in interest of the Holders
requesting registration, addressed to the underwriters, if any, and to the
Holders requesting registration of Registrable Securities and (ii) a letter
dated as of such date, from the independent certified public accountants of the
Company, in form and substance as is customarily given by independent certified
public accountants to underwriters in connection with an underwritten public
offering, addressed to the underwriters, if any, and if permitted by applicable
accounting standards, to the Holders requesting registration of Registrable
Securities.

          3.10 Indemnification.

               (a)  The Company will indemnify each Holder, each of its
officers, directors and partners, and each person controlling such Holder within
the meaning of Section 15 of the Securities Act, including, without limitation,
any Investment Advisor (as defined in the Investment Company Act of 1940)
controlling any Holder, with respect to which registration, qualification or
compliance has been effected pursuant to this Section 3, and each underwriter,
if any, and each person who controls any underwriter within the meaning of
Section 15 of the Securities Act, against all expenses, claims, losses, damages
or liabilities (or actions in respect thereof), including any of the foregoing
incurred in settlement of any litigation, commenced or threatened, arising out
of or based on any untrue statement (or alleged untrue statement) of a material
fact contained in any registration statement, prospectus, offering circular or
other document, or any amendment or supplement thereto, incident to any such
registration, qualification or compliance, or based on any omission (or alleged
omission) to state therein a material fact required to be stated therein or
necessary to make the statements therein, in light of the circumstances in which
they were made, not misleading, or any violation by the Company of the
Securities Act or any rule or regulation promulgated under the Securities Act
applicable to the Company in connection


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<PAGE>   10

with any such registration, qualification or compliance, and the Company will
reimburse each such Holder, each of its officers, directors, partners and each
person controlling such Holder, each such underwriter and each person who
controls any such underwriter, for any legal and any other expenses reasonably
incurred in connection with investigating, preparing or defending any such
claim, loss, damage, liability or action, provided that the Company will not be
liable in any such case to the extent that any such claim, loss, damage,
liability or expense arises out of or is based on any untrue statement or
omission or alleged untrue statement or omission, made in reliance upon and in
conformity with written information furnished to the Company by an instrument
duly executed by such Holder, controlling person or underwriter specifically for
use therein, or the failure of such Holder to deliver a Prospectus that was
delivered to the Holder prior to a sale or sales by such Holder.

               (b)  Each Holder will, if Registrable Securities held by such
Holder are included in the securities as to which such registration,
qualification or compliance is being effected, indemnify the Company, each of
its directors and officers, each underwriter, if any, of the Company's
securities covered by such a registration statement, each person who controls
the Company or such underwriter within the meaning of Section 15 of the
Securities Act, and each other Holder, each of its officers, directors, partners
and each person controlling such Holder within the meaning of Section 15 of the
Securities Act, against all claims, losses, damages and liabilities (or actions
in respect thereof) arising out of or based on any untrue statement (or alleged
untrue statement) of a material fact contained in any such registration
statement, prospectus, offering circular or other document, or any omission (or
alleged omission) to state therein a material fact required to be stated therein
or necessary to make the statements therein not misleading, and will reimburse
the Company, such Holders, such directors, officers, persons, underwriters or
control persons for any legal or any other expenses reasonably incurred in
connection with investigating or defending any such claim, loss, damage,
liability or action, in each case to the extent, but only to the extent, that
such untrue statement (or alleged untrue statement) or omission (or alleged
omission) is made in such registration statement, prospectus, offering circular
or other document in reliance upon and in conformity with written information
furnished to the Company by an instrument duly executed by such Holder
specifically for use therein. Notwithstanding the foregoing, the liability of
each Holder under this subsection (b) shall be limited to the proportion of any
such loss, claim, damage, liability or expense which is equal to the proportion
that the public offering price of the shares sold by such Holder under such
registration statement bears to the total public offering price of all
securities sold thereunder, but not to exceed the proceeds received by such
Holder from the sale of Registrable Securities covered by such registration
statement unless such liability resulted from willful misconduct by such Holder.
A Holder will not be required to enter into any agreement or undertaking in
connection with any registration under this Section 3 providing for any
indemnification or contribution on the part of such Holder greater than the
Holder's obligations under this Section 3.10(b).

               (c)  Each party entitled to indemnification under this Section
3.10 (the "INDEMNIFIED PARTY") shall give notice to the party required to
provide indemnification (the "INDEMNIFYING PARTY") promptly after such
Indemnified Party has actual knowledge of any claim as to which indemnity may be
sought, and shall permit the Indemnifying Party to assume the defense of any
such claim or any litigation resulting therefrom, provided that counsel for the
Indemnifying Party, who shall conduct the defense of such claim or litigation,
shall be approved by the


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<PAGE>   11

Indemnified Party (whose approval shall not unreasonably be withheld), and the
Indemnified Party may participate in such defense at such party's expense, and
provided further that the failure of any Indemnified Party to give notice as
provided herein shall not relieve the Indemnifying Party of its obligations
under this Section 3 unless the failure to give such notice is materially
prejudicial to an Indemnifying Party's ability to defend such action and
provided further, that the Indemnifying Party shall not assume the defense for
matters as to which there is a conflict of interest or separate and different
defenses but shall bear the expense of such defense nevertheless. No
Indemnifying Party, in the defense of any such claim or litigation, shall,
except with the consent of each Indemnified Party, consent to entry of any
judgment or enter into any settlement which does not include as an unconditional
term thereof the giving by the claimant or plaintiff to such Indemnified Party
of a release from all liability in respect to such claim or litigation.

               (d)  If the indemnification provided for in paragraphs (a)
through (c) of this Section 3.10 is unavailable or insufficient to hold harmless
an indemnified party under such paragraphs in respect of any losses, claims,
damages or liabilities or actions in respect thereof referred to therein, then
each indemnifying party shall in lieu of indemnifying such indemnified party
contribute to the amount paid or payable by such indemnified party as a result
of such losses, claims, damages, liabilities or actions in such proportion as
appropriate to reflect the relative fault of the Company, on the one hand, and
the underwriters and the Holder of such Registrable Securities, on the other, in
connection with the statements or omissions which resulted in such losses,
claims, damages, liabilities or actions as well as any other relevant equitable
considerations, including the failure to give any notice under paragraph (c).
The relative fault shall be determined by reference to, among other things,
whether the untrue or alleged untrue statement of a material fact relates to
information supplied by the Company, on the one hand, or the underwriters or the
Holders of such Registrable Securities, on the other, and to the parties'
relative intent, knowledge, access to information and opportunity to correct or
prevent such statement or omission. The Company and each of the Holders agrees
that it would not be just and equitable if contributions pursuant to this
paragraph were determined by pro rata allocation (even if all of the Holders of
such Registrable Securities were treated as one entity for such purpose) or by
any other method of allocation which did not take account of the equitable
considerations referred to above in this paragraph. The amount paid or payable
by an indemnified party as a result of the losses, claims, damages, liabilities
or action in respect thereof, referred to above in this paragraph, shall be
deemed to include any legal or other expenses reasonably incurred by such
indemnified party in connection with investigating or defending any such action
or claim. Notwithstanding the provisions of this paragraph, no Holder shall be
required to contribute any amount in excess of the lesser of (i) the proportion
that the public offering price of shares sold by such Holder under such
registration statement bears to the total public offering price of all
securities sold thereunder, but not to exceed the proceeds received by such
Holder for the sale of Registrable Securities covered by such registration
statement and (ii) the amount of any damages which they would have otherwise
been required to pay by reason of such untrue or alleged untrue statement or
omission. No person guilty of fraudulent misrepresentations (within the meaning
of Section 11(f) of the Securities Act), shall be entitled to contribution from
any person who is not guilty of such fraudulent misrepresentation.

          3.11 Information by Holder. The Holder or Holders of Registrable
Securities included in any registration shall furnish to the Company such
information regarding such Holder or Holders, the Registrable Securities held by
them and the distribution proposed by such Holder or


                                      -11-

<PAGE>   12

Holders as the Company may reasonably request in writing and as shall be
required in connection with any registration, qualification or compliance
referred to in this Section 3.

          3.12 Rule 144 Reporting. With a view to making available the benefits
of certain rules and regulations of the Commission which may at any time permit
the sale of the Restricted Securities to the public without registration, after
such time as a public market exists for the Common Stock of the Company, the
Company agrees to use its best efforts to:

               (a)  Make and keep public information available, as those terms
are understood and defined in Rule 144 under the Securities Act, at all times
after the effective date that the Company becomes subject to the reporting
requirements of the Securities Act or the Securities Exchange Act of 1934, as
amended.

               (b)  Use its best efforts to file with the Commission in a timely
manner all reports and other documents required of the Company under the
Securities Act and the Securities Exchange Act of 1934, as amended (at any time
after it has become subject to such reporting requirements);

               (c)  So long as a Purchaser owns any Restricted Securities to
furnish to the Purchaser forthwith upon request a written statement by the
Company as to its compliance with the reporting requirements of said Rule 144
(at any time after 90 days after the effective date of the first registration
statement filed by the Company for an offering of its securities to the general
public), and of the Securities Act and the Securities Exchange Act of 1934 (at
any time after it has become subject to such reporting requirements), a copy of
the most recent annual or quarterly report of the Company, and such other
reports and documents of the Company and other information in the possession of
or reasonably obtainable by the Company as a Purchaser may reasonably request in
availing itself of any rule or regulation of the Commission allowing a Purchaser
to sell any such securities without registration.

          3.13 Transfer of Registration Rights. The rights to cause the Company
to register securities granted Holders under Sections 3.5, 3.6 and 3.7 may be
assigned to a transferee or assignee in connection with any transfer or
assignment of Registrable Securities by a Holder of not less than 100 shares of
Registrable Securities, or to any transferee or assignee who is a subsidiary,
parent, shareholder or constituent partner of a Holder or a trust for the
benefit of such Holder or partner (or the estate of such person), provided that
such transfer may otherwise be effected in accordance with applicable securities
laws.

          3.14 Standoff Agreement. Each Holder agrees, in connection with the
Company's initial public offering of the Company's securities, not to sell, make
any short sale of, loan, grant any option for the purchase of, or otherwise
dispose of any shares of capital stock of the Company, including, but not
limited to, the Shares and the Conversion Stock (other than those included in
the registration), without the prior written consent of the underwriters, for
one hundred eighty (180) days) from the effective date of such registration;
provided, that the officers and directors of the Company who own stock of the
Company or the right to acquire stock of the Company also agree to such
restrictions. Each Holder further agrees that the Company may impose stop
transfer instructions in order to enforce the foregoing covenant.


                                      -12-

<PAGE>   13

          3.15 Limitations on Subsequent Registration Rights. From and after the
date of this Agreement, the Company shall not, without the prior written consent
of the Holders of a majority of the outstanding Registrable Securities, enter
into any agreement with any holder or prospective holder of any securities of
the Company which would allow such holder or prospective holder (a) to include
such securities in any registration filed under Section 3.5, 3.6 or 3.7 hereof,
unless under the terms of such agreement, such holder or prospective holder may
include such securities in any such registration only to the extent that the
inclusion of his securities will not reduce the amount of the Registrable
Securities of the Holders which is included, or (b) to make a demand
registration which could result in such registration statement being declared
effective prior to the earlier of either of the date set forth in Section
3.5(a).

          3.16 Termination of Registration Rights. The rights granted under this
Section 3 shall terminate on the earlier to occur of the following: (i) on the
fifth anniversary of the consummation of the initial underwritten public
offering of the Company's securities pursuant to a registration statement filed
under the Securities Act; or (ii) as to a particular Holder, when such Holder is
eligible to sell all of its Registrable Securities within any 90 day period in
reliance on Rule 144 under the Securities Act, provided the company has
consummated an initial underwritten public offering prior to such date.

          3.17 Right of First Offer. Subject to the terms and conditions
specified in this Section 3.17, the Company hereby grants to each Purchaser a
right of first offer with respect to future sales by the Company of its Shares
(as hereinafter defined). For purposes of this Section 3.17, Purchaser includes
any partners and affiliates of a Purchaser. A Purchaser shall be entitled to
apportion the right of first offer hereby granted it among itself and its
partners and affiliates in such proportions as it deems appropriate.

     Each time the Company proposes to offer any shares of, or securities
convertible into or exercisable for any shares of, any class of its capital
stock ("Shares"), the Company shall first make an offering of such Shares to
each Purchaser in accordance with the following provisions:

               (a)  The Company shall deliver a notice by certified mail
("Notice") to the Purchasers stating (i) its bona fide intention to offer such
Shares, (ii) the number of such Shares to be offered, and (iii) the price and
terms, if any, upon which it proposes to offer such Shares.

               (b)  Within 20 calendar days after receipt of the Notice, the
Purchaser may elect to purchase or obtain, at the price and on the terms
specified in the Notice, up to that portion of such Shares which equals the
proportion that the number of shares of Common Stock issued and held or issuable
upon conversion of the Preferred Stock then held, by such Purchaser bears to the
total number of shares of Common Stock of the Company outstanding on the date of
this Agreement (assuming full conversion and exercise of all convertible or
exercisable securities). The Company shall promptly, in writing, inform each
Purchaser which purchases all the shares available to it ("Fully Exercising
Purchaser") of any other Purchaser's failure to do likewise. During the ten-day
period commencing after such information is given, each Fully-Exercising
Purchaser shall be entitled to obtain that portion of the Shares for which
Purchasers were entitled to subscribe but which were not subscribed for by the
Purchasers which is equal to the proportion that the number of shares of common
stock issued and held, or issuable upon conversion of Preferred Stock then held,
by such Fully-Exercising Purchaser bears to the total number of shares of common


                                      -13-

<PAGE>   14

stock issued and held, or issuable upon conversion of the Preferred Stock then
held, by all Fully-Exercising Purchasers who wish to purchase some of the
unsubscribed shares.

               (c)  If all Shares that Purchasers are entitled to obtain
pursuant to subsection 3.17(b) are not elected to be obtained as provided in
subsection 3.17(b) hereof, the Company may, during the 60-day period following
the expiration of the period provided in subsection 3.17(b) hereof, offer the
remaining unsubscribed portion of such Shares to any person or persons at a
price not less than, and upon terms no more favorable to the offeree than those
specified in the Notice. If the Company does not enter into an agreement for the
sale of the Shares within such period, or if such agreement is not consummated
within 30 days of the execution thereof, the right provided hereunder shall be
deemed to be revived and such Shares shall not be offered unless first reoffered
to the Purchasers in accordance herewith.

               (d)  The right of first offer in this Section 3.17 shall not be
applicable (i) to the issuance or sale of shares of Series F Preferred Stock;
(ii) to the issuance or sale of shares of common stock (or options therefor) to
officers, directors, employees, scientific advisors, or consultants for the
primary purpose of soliciting or retaining their employment or services,
provided each such officer, director, employee, scientific advisor, or
consultant executes an agreement in the form then approved by the Company's
Board of Directors and such grant or issuance is approved by the Company's Board
of Directors; (iii) to or after consummation of a bona fide, firmly underwritten
public offering of shares of common stock, registered under the Act pursuant to
a registration statement on Form S-1; (iv) the issuance of securities pursuant
to the conversion or exercise of convertible or exercisable securities
outstanding on the date of this Agreement; (v) the issuance of securities in
connection with a bona fide business acquisition of or by the Company, whether
by merger, consolidation, sale of assets, sale or exchange of stock or
otherwise; (vi) the issuance of stock, warrants or other securities or rights to
persons or entities with which the Company has business relationships (such as
personal property and equipment lease lines) provided such issuances are for
other than primarily equity financing purposes.

               (e)  The right of first offer set forth in this Section 3.17 may
not be assigned or transferred. 4. Affirmative Covenants of the Company and the
Purchasers

     The Company hereby covenants and agrees as follows:

          4.1  Financial Information.

               (a)  The Company will provide each Purchaser with reports set
forth below:

                    (i)  as soon as practicable after the end of each fiscal
year, and in any event within 120 days thereafter, consolidated balance sheets
of the Company and its subsidiaries, if any, as of the end of such fiscal year,
and consolidated statements of income and consolidated statements of changes in
financial position of the Company and its subsidiaries, if any,


                                      -14-

<PAGE>   15

for such year, prepared in accordance with generally accepted accounting
principles, all in reasonable detail and audited by independent public
accountants of national standing selected by the Company; and

                    (ii) as soon as practicable after the end of each quarter,
and in any event within 90 days after each quarterly accounting period, an
unaudited quarterly report including a balance sheet, profit and loss statement
and cash flow analysis (prepared in accordance with generally accepted
accounting principles other than for accompanying notes and subject to changes
resulting from year-end audit adjustments), setting forth in comparative form
the budgeted figures for the fiscal period then reported.

               (b)  So long as a Purchaser continues to hold at least 100
Shares, the Company will provide each Purchaser with reports set forth below:

                    (i)  as soon as practicable after the end of each month, and
in any event within 25 days thereafter, consolidated balance sheets of the
Company and its subsidiaries, if any, as of the end of such period, and
consolidated statements of income and consolidated statements of changes in
financial position of the Company and its subsidiaries, if any, for such period,
prepared in accordance with generally accepted accounting principles, setting
forth in comparative form the budgeted figures for the fiscal period then
reported, all in reasonable detail.

                    (ii) as soon as practicable, and in any event within 30 days
prior to the beginning of the Company's fiscal year, the annual operating plan.

          4.2  Assignment of Rights to Financial Information. The rights granted
pursuant to Section 4.1 may not be assigned or otherwise conveyed by any
Purchaser or by any subsequent transferee of any such rights without the prior
written consent of the Company; provided, however, that any Purchaser may assign
to any constituent partner of a Purchaser, other than a competitor of the
Company, and after giving notice to the Company, the rights granted pursuant to
Section 4.1.

          4.3  Termination of Covenants. The covenants set forth in Section 4.1
shall terminate and be of no further force or effect upon the closing of the
Company's initial underwritten public offering pursuant to an effective
registration statement filed by the Company under the Securities Act.

     5.   Miscellaneous.

          5.1  Waivers and Amendments. With the written consent of the Company
and the record holders of more than fifty percent (50%) of the Registrable
Securities, the obligations of the Company and the rights of the holders of the
Registrable Securities under this Agreement may be waived (either generally or
in a particular instance, either retroactively or prospectively and either for a
specified period of time or indefinitely), and with the same consent the
Company, when authorized by resolution of its Board of Directors, may enter into
a supplementary agreement for the purpose of adding any provisions to or
changing in any manner or eliminating any of the provisions of this Agreement;
provided, however, that (A) any provision added, changed or eliminated pursuant
to this Section 5 shall also be subject to the approval of the record holders of
more than fifty percent


                                      -15-

<PAGE>   16

(50%) of any class or series of the Company's stock who are parties to this
Agreement and whose rights are negatively affected by any such addition, change
or elimination, and (B) no such waiver or supplemental agreement shall reduce
the aforesaid percentage of the Registrable Securities, the holders of which are
required to consent to any waiver or supplemental agreement without the consent
of the record holders of all of the Registrable Securities. Upon the
effectuation of each such waiver, consent, agreement, amendment or modification
the Company shall promptly given written notice thereof to the record holders of
the Registrable Securities who have not previously consented thereto in writing.
Neither this Agreement nor any provisions hereof may be changed, waived,
discharged or terminated orally, but only by a signed statement in writing.

          5.2  Governing Law. This Agreement shall be governed in all respects
by the laws of the State of California.

          5.3  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.

          5.4  Entire Agreement. This Agreement constitutes the full and entire
understanding and agreement between the parties with regard to the subjects
hereof and thereof.

          5.5  Notices. All notices and other communications required or
permitted hereunder shall be effective upon receipt and shall be in writing and
may be delivered in person, by telecopy, electronic mail, overnight delivery
service or U.S. mail, in which event it may be mailed by first-class, certified
or registered, postage prepaid, addressed (a) if to a Purchaser or Holder, at
such Purchaser's or Holder's address set forth in the applicable Investment
Agreement or the Series F Agreement, or at such other address as such Purchaser
or Holder shall have furnished the Company in writing, or (b) if to the Company,
at its address set forth on the signature page of this Agreement, or at such
other address as the Company shall have furnished to the Purchasers, Holders and
each such other Holder in writing. Notwithstanding the foregoing, all notices
and communications to addresses outside the United States shall be given by
telecopier and confirmed in writing sent by overnight or two-day courier
service.

          5.6  Titles and Subtitles. The titles of the paragraphs and
subparagraphs of this Agreement are for convenience of reference only and are
not to be considered in construing this Agreement.

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

          5.8  Disclaimer of Liability. All liabilities of Janus Investment Fund
(the "Fund") arising directly or indirectly under this Agreement, of any and
every nature whatsoever, shall be satisfied solely out of the assets of the Fund
and that no trustee, officer or holder of shares of beneficial interest of the
Fund shall be personally liable for any of the foregoing liabilities. The Fund's
Declaration of Trust, which sets forth the respective rights and limitations on
liability of each party, is on file with the Office of the Secretary of the
Commonwealth of Massachusetts.


                                      -16-

<PAGE>   17

                                        "COMPANY"

                                        Third Wave Technologies, Inc.
                                        502 South Rosa Road
                                        Madison, Wisconsin  53719-1256

                                        By:
                                           -------------------------------------
                                           Dr. Lance Fors,
                                           Chief Executive Officer





THIRD WAVE TECHNOLOGIES, INC.
INVESTORS' RIGHTS AGREEMENT SIGNATURE PAGE

<PAGE>   18

                                        "INVESTOR" OR "HOLDER"


                                        By:
                                           -------------------------------------
                                           Name:
                                           Title:





THIRD WAVE TECHNOLOGIES, INC.
INVESTORS' RIGHTS AGREEMENT SIGNATURE PAGE

<PAGE>   19

                                    EXHIBIT 1

                         EXISTING PREFERRED STOCKHOLDERS





Venture Investors of Wisconsin

The Wellcome Trust Limited, as trustee of The Wellcome Trust

Schroder Ventures International Life Sciences Fund II LP1

UK Medical Ventures Fund No. 1 LP

S.R. One, Limited

Burrill Agbio Capital Fund

M & I Capital Markets Group, Inc.

Schroder Ventures International Life Sciences Fund II LP2

Venture Investors Early Stage Fund II Limited Partnership

Venture Investors Early Stage II Limited Partnership






THIRD WAVE TECHNOLOGIES, INC.
INVESTORS' RIGHTS AGREEMENT SIGNATURE PAGE