<PAGE>   1
EXHIBIT 10.56

                          REGISTRATION RIGHTS AGREEMENT

                                      AMONG

                                BIO-PLEXUS, INC.

                                       AND

                                THE STOCKHOLDERS

                           LISTED ON EXHIBIT A HERETO

                           Dated as of July ___, 2001
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                  THIS REGISTRATION RIGHTS AGREEMENT, dated as of July __, 2001,
is made among Bio-Plexus, Inc., a Delaware corporation (the "Reorganized
Company"), and the stockholders of the Reorganized Company listed on Exhibit A
hereto (the "Stockholders").

                  WHEREAS, on April 4, 2001, Bio-Plexus, Inc. a Connecticut
corporation (the "Company"), filed a voluntary petition (Case No. 01-21079)
under chapter 11 of the United States Bankruptcy Code, as in effect on that date
(the "Bankruptcy Code"), with the United States Bankruptcy Court for the
District of Connecticut, Hartford Division (the "Bankruptcy Court").

                  WHEREAS, on June 12, 2001 the Company's First Amended Plan of
Reorganization, dated June 12, 2001 (the "Plan"), was confirmed by the order of
the Bankruptcy Court pursuant to Section 1129 of the Bankruptcy Code;

                  WHEREAS, pursuant to Article V, paragraph D of the Plan, on
the Effective Date (as defined in the Plan), the Company was reincorporated as a
Delaware corporation by means of a merger by and between the Company and the
Reorganized Company, a newly created wholly owned subsidiary of the Company;

                  WHEREAS, pursuant to Article IV, paragraph E of the Plan, on
the Effective Date, the Reorganized Company issued to the Stockholders 8,501,224
shares of Common Stock (as defined below);

                  WHEREAS, Article V, paragraph B of the Plan provides that,
immediately following the Effective Date, the Reorganized Company shall issue to
the Stockholders 1,314,060 shares of Common Stock;

                  WHEREAS, if any of the Stockholders desire to sell shares of
Common Stock, it may be necessary to register such shares under the Securities
Act (as defined below); and

                  WHEREAS, as part of, and as consideration for, its consent to
the Plan and the acquisition of shares of Common Stock by the Stockholders from
the Reorganized Company on the date hereof and from time to time hereafter, the
Reorganized Company hereby grants to the Stockholders certain registration and
other rights with respect to their shares of Common Stock as more fully set
forth herein.

                  Accordingly, the parties hereto agree as follows:

                  1. Definitions. As used herein, unless the context otherwise
requires, the following terms have the following respective meanings:
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                  "Certificate of Incorporation" means the Certificate of
Incorporation of the Reorganized Company, as it may be amended or restated
hereafter from time to time.

                  "Commission" means the Securities and Exchange Commission or
any other Federal agency at the time administering the Securities Act.

                  "Common Stock" means any shares of common stock, par value
$.001 per share, of the Reorganized Company, now or hereafter authorized to be
issued, and any and all securities of any kind whatsoever of the Reorganized
Company which may be exchanged for or converted into Common Stock (including,
without limitation the Warrant Stock), any and all securities of any kind
whatsoever of the Reorganized Company which may be issued on or after the date
hereof in respect of, in exchange for, or upon conversion of shares of Common
Stock pursuant to a merger, consolidation, stock split, stock dividend,
recapitalization of the Reorganized Company or otherwise.

                  "Exchange Act" means the Securities Exchange Act of 1934, 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. Reference
to a particular section of the Exchange Act shall include a reference to the
comparable section, if any, of any such similar federal statute.

                  "Other Investor" means each Person who, at the time of any
registration of Common Stock hereunder, has the right under a stockholder's
agreement or stock option agreement with the Reorganized Company or any
subsidiary thereof to participate in any public offering in which all or a
portion of the shares of Common Stock owned by the Stockholders are registered
under the Securities Act.

                  "Person" means a corporation, an association, a partnership,
an organization, a business, a trust, an individual, or any other entity or
organization, including a government or political subdivision or an
instrumentality or agency thereof.

                  "Registrable Securities" means (i) any shares of Common Stock
owned by the Stockholders, (ii) any shares of Common Stock issuable upon the
conversion of any securities held by the Stockholders convertible into Common
Stock, (iii) any shares of Common Stock held pursuant to the terms of a
stockholder's agreement or issuable upon exercise of an option pursuant to the
terms of a stock option agreement, as the case may be, between any Other
Investor and the Reorganized Company or any subsidiary thereof, which agreement
gives such Other Investor the right to participate proportionately with the
Stockholders in a public offering with respect to such shares, and (iv) any
Common Stock issued with respect to the Common Stock referred to in clauses (i),
(ii) or (iii) by way of a stock dividend, stock split or reverse stock split or
in connection with a combination of shares, recapitalization, merger,
consolidation or otherwise. As to any particular Registrable Securities, such
securities shall cease to be Registrable Securities (a) when a registration
statement with respect to the sale of such securities shall have
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become effective under the Securities Act and such securities shall have been
disposed of in accordance with such registration statement, (b) when such
securities shall have been otherwise transferred, new certificates for them not
bearing a legend restricting further transfer shall have been delivered by the
Reorganized Company and subsequent public distribution of them shall not require
registration of them under the Securities Act, or (c) when such securities shall
have been sold as permitted by, and in compliance with, the Securities Act. Any
certificate evidencing the Registrable Securities shall bear a legend stating
that the securities have not been registered under the Securities Act and
setting forth or referring to the restrictions on transferability and sale of
the securities.

                  "Registration Expenses" means all expenses incident to the
registration and disposition of the Registrable Securities pursuant to Section 2
hereof, including, without limitation, all registration, filing and applicable
national securities exchange fees, all fees and expenses of complying with state
securities or blue sky laws (including fees and disbursements of counsel to the
underwriters or the Stockholders and the Other Investors in connection with
"blue sky" qualification of the Registrable Securities and determination of
their eligibility for investment under the laws of the various jurisdictions),
all word processing, duplicating and printing expenses, all messenger and
delivery expenses, the fees and disbursements of counsel for the Reorganized
Company and of its independent public accountants, including the expenses of
"cold comfort" letters or any special audits required by, or incident to, such
registration, all fees and disbursements of underwriters (other than
underwriting discounts and commissions), all transfer taxes, and the fees and
expenses of counsel to the Stockholders and the Other Investors; provided,
however, that Registration Expenses shall exclude, and the Stockholders and the
Other Investors shall pay, underwriting discounts and commissions in respect of
the Registrable Securities being registered.

                  "Securities Act" means 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. References to a
particular section of the Securities Act shall include a reference to the
comparable section, if any, of any such similar Federal statute.

                  "Warrant Stock" shall mean the shares of Common Stock
purchased by the holders of the warrants issued to the Stockholders in
connection with the Plan.

                  2.     Registration Under Securities Act, etc.

                           2.1      Registration on Request.

                           (a) Request. At any time or from time to time, the
Stockholders, individually or jointly, shall have the right to require the
Reorganized Company to effect the registration under the Securities Act of all
or part of the Registrable Securities, by delivering a written request therefor
to the Reorganized
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Company specifying the number of shares of Registrable Securities and the
intended method of distribution. The Reorganized Company shall, (i) as
expeditiously as possible (but in any event within 120 days of receipt of a
written request), use its best efforts to effect the registration under the
Securities Act (including by means of a shelf registration pursuant to Rule 415
under the Securities Act if so requested in such request and if the Reorganized
Company is then eligible to use such a registration) of the Registrable
Securities which the Reorganized Company has been so requested to register by
the Stockholders, for distribution in accordance with the intended method of
distribution set forth in the written request delivered by the Stockholders, and
(ii) if requested by the Stockholders, obtain acceleration of the effective date
of the registration statement relating to such registration.

                           (b) Registration of Other Securities. Whenever the
Reorganized Company shall effect a registration pursuant to this Section 2.1 in
connection with an underwritten offering by any Stockholder and any Other
Investors of Registrable Securities, no securities other than Registrable
Securities shall be included among the securities covered by such registration
unless the Stockholder or Stockholders so registering Registrable Securities
(the "Registering Stockholders") shall have consented in writing to the
inclusion therein of such other securities, which consent may be subject to
terms and conditions determined by the Registering Stockholders in their sole
discretion.

                           (c) Registration Statement Form. Registrations under
this Section 2.1 shall be on such appropriate registration form of the
Commission as shall be selected by the Reorganized Company and as shall be
reasonably acceptable to the Registering Stockholders. The Reorganized Company
agrees to include in any such registration statement all information which, in
the opinion of counsel to the Registering Stockholders and counsel to the
Reorganized Company, is necessary or desirable to be included therein.

                           (d) Expenses. The Reorganized Company shall pay all
Registration Expenses in connection with any registration requested pursuant to
this Section 2.1.

                           (e) Effective Registration Statement. A registration
requested pursuant to this Section 2.1 shall not be deemed to have been effected
(including for purposes of paragraph (h) of this Section 2.1) (i) unless a
registration statement with respect thereto has become effective and has been
kept continuously effective for a period of at least 120 days (or such shorter
period which shall terminate when all the Registrable Securities covered by such
registration statement have been sold pursuant thereto), (ii) if after it has
become effective, such registration is interfered with by any stop order,
injunction or other order or requirement of the Commission or other governmental
agency or court for any reason not attributable to the Registering Stockholders
and has not thereafter become effective, or (iii) if the conditions to closing
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specified in the underwriting agreement, if any, entered into in connection with
such registration are not satisfied or waived.

                           (f) Selection of Underwriters. The underwriters of
each underwritten offering of the Registrable Securities to be registered shall
be selected by the Registering Stockholders.

                           (g) Right to Withdraw. If the managing underwriter of
any underwritten offering shall advise the Registering Stockholders that the
Registrable Securities covered by the registration statement cannot be sold in
such offering within a price range acceptable to the Registering Stockholders,
then the Registering Stockholders shall have the right to notify the Reorganized
Company in writing that they have determined that the registration statement be
abandoned or withdrawn, in which event the Reorganized Company shall abandon or
withdraw such registration statement. In the event of such abandonment or
withdrawal, such request shall not be counted for purposes of the requests for
registration to which the Stockholders are entitled pursuant to this Section
2.1.

                           (h) Limitations on Registration on Request. The
Stockholders shall be entitled to require the Reorganized Company to effect, and
the Reorganized Company shall be required to effect, six (6) registrations in
the aggregate pursuant to this Section 2.1.

                           (i) Postponement. The Reorganized Company shall be
entitled once in any six-month period to postpone for a reasonable period of
time (but not exceeding 90 days) (the "Postponement Period") the filing of any
registration statement required to be prepared and filed by it pursuant to this
Section 2.1 if the Reorganized Company determines, in its reasonable judgment,
that such registration and offering would materially interfere with any material
financing, corporate reorganization or other material transaction involving the
Reorganized Company or any subsidiary, or would require premature disclosure
thereof, and promptly gives the Registering Stockholders written notice of such
determination, containing a general statement of the reasons for such
postponement and an approximation of the anticipated delay. If the Reorganized
Company shall so postpone the filing of a registration statement, the
Stockholders shall have the right to withdraw the request for registration by
giving written notice to the Reorganized Company at any time and, in the event
of such withdrawal, such request shall not be counted for purposes of the
requests for registration to which the Stockholders are entitled pursuant to
this Section 2.1.

                  2.2 Incidental Registration.

                           (a) Right to Include Registrable Securities. If the
Reorganized Company at any time proposes to register any of its securities under
the Securities Act by registration on Form S-1, S-2 or S-3 or any successor or
similar form(s)
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(except registrations on any such Form or similar form(s) solely for
registration of securities in connection with an employee benefit plan or
dividend reinvestment plan or a merger or consolidation), whether or not for
sale for its own account, it will each such time give prompt written notice to
each of the Stockholders of its intention to do so and of the Stockholders'
rights under this Section 2.2. Upon the written request of any of the
Stockholders (which request shall specify the maximum number of Registrable
Securities intended to be disposed of by the Stockholders), made as promptly as
practicable and in any event within 30 days after the receipt of any such notice
(15 days if the Reorganized Company states in such written notice or gives
telephonic notice to the Stockholders, with written confirmation to follow
promptly thereafter, stating that (i) such registration will be on Form S-3 and
(ii) such shorter period of time is required because of a planned filing date),
the Reorganized Company shall use its best efforts to effect the registration
under the Securities Act of all Registrable Securities which the Reorganized
Company has been so requested to register by the Stockholders; provided,
however, that if, at any time after giving written notice of its intention to
register any securities and prior to the effective date of the registration
statement filed in connection with such registration, the Reorganized Company
shall determine for any reason not to register or to delay registration of such
securities, the Reorganized Company shall give written notice of such
determination and its reasons therefor to the Stockholders and (i) in the case
of a determination not to register, shall be relieved of its obligation to
register any Registrable Securities in connection with such registration (but
not from any obligation of the Reorganized Company to pay the Registration
Expenses in connection therewith), without prejudice, however, to the rights of
the Stockholders to request that such registration be effected as a registration
under Section 2.1 and (ii) in the case of a determination to delay registering,
shall be permitted to delay registering any Registrable Securities, for the same
period as the delay in registering such other securities. No registration
effected under this Section 2.2 shall relieve the Reorganized Company of its
obligation to effect any registration upon request under Section 2.1. The
Reorganized Company will pay all Registration Expenses in connection with any
registration of Registrable Securities requested pursuant to this Section 2.2.

                           (b) Right to Withdraw. The Stockholders shall have
the right to withdraw their request for inclusion of its Registrable Securities
in any registration statement pursuant to this Section 2.2 at any time prior to
the execution of an underwriting agreement with respect thereto by giving
written notice to the Reorganized Company of its request to withdraw.

                           (c) Priority in Incidental Registrations. If the
managing underwriter of any underwritten offering shall inform the Reorganized
Company by letter of its belief that the number of Registrable Securities
requested to be included in such registration, when added to the number of other
securities to be offered in such registration, would materially adversely affect
such offering, then the Reorganized Company shall include in such registration,
to the extent of the number and type which
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the Reorganized Company is so advised can be sold in (or during the time of)
such offering without so materially adversely affecting such offering (the
"Section 2.2 Sale Amount"), (i) all of the securities proposed by the
Reorganized Company to be sold for its own account; (ii) thereafter, to the
extent the Section 2.2 Sale Amount is not exceeded, the Registrable Securities
requested by the Stockholders to be included in such registration pursuant to
Section 2.2(a) (including Registrable Securities held by Other Investors); and
(iii) thereafter, to the extent the Section 2.2 Sale Amount is not exceeded, any
other securities of the Reorganized Company requested to be included in such
registration by any holder thereof, including, in the case where such
registration is to be effected as a result of the exercise by a holder of the
Reorganized Company's securities of such holder's right to cause such securities
to be so registered, the securities of such holder.

                           (d) Plan of Distribution. Any participation by
holders of Registrable Securities in a registration by the Reorganized Company
shall be in accordance with the Reorganized Company's plan of distribution,
provided that the Registering Stockholders shall have the right to select the
co-managing underwriter.


                  2.3 Registration Procedures. If and whenever the Reorganized
Company is required to use its best efforts to effect the registration of any
Registrable Securities under the Securities Act as provided in Sections 2.1 and
2.2 hereof, the Reorganized Company shall as expeditiously as possible:

                           (a) prepare and file with the Commission as soon as
practicable the requisite registration statement to effect such registration
(and shall include all financial statements required by the Commission to be
filed therewith) and thereafter use its best efforts to cause such registration
statement to become effective; provided, however, that before filing such
registration statement (including all exhibits) or any amendment or supplement
thereto or comparable statements under securities or blue sky laws of any
jurisdiction, the Reorganized Company shall furnish such documents to the
Registering Stockholders and each underwriter, if any, participating in the
offering of the Registrable Securities and their respective counsel, which
documents will be subject to the review and comments of the Registering
Stockholders, each underwriter and their respective counsel; and provided,
further, however, that the Reorganized Company may discontinue any registration
of its securities which are not Registrable Securities at any time prior to the
effective date of the registration statement relating thereto;

                           (b) notify the Registering Stockholders of the
Commission's requests for amending or supplementing the registration statement
and the prospectus, and prepare and file with the Commission such amendments and
supplements to such registration statement and the prospectus used in connection
therewith as may be necessary to keep such registration statement effective and
to comply with the provisions of the Securities Act with respect to the
disposition of all Registrable Securities covered
<PAGE>   9
by such registration statement for such period as shall be required for the
disposition of all of such Registrable Securities in accordance with the
intended method of distribution thereof; provided, that except with respect to
any such registration statement filed pursuant to Rule 415 under the Securities
Act, such period need not exceed 120 days;

                           (c) furnish, without charge, to the Registering
Stockholders and each underwriter such number of conformed copies of such
registration statement and of each such amendment and supplement thereto (in
each case including all exhibits), such number of copies of the prospectus
contained in such registration statement (including each preliminary prospectus
and any summary prospectus) and any other prospectus filed under Rule 424 under
the Securities Act, in conformity with the requirements of the Securities Act,
and such other documents, as the Registering Stockholders and such underwriters
may reasonably request;

                           (d) use its best efforts (i) to register or qualify
all Registrable Securities and other securities covered by such registration
statement under such securities or blue sky laws of such States of the United
States of America where an exemption is not available and as the Registering
Stockholders or any managing underwriter shall reasonably request, (ii) to keep
such registration or qualification in effect for so long as such registration
statement remains in effect, and (iii) to take any other action which may be
reasonably necessary or advisable to enable the Registering Stockholders to
consummate the disposition in such jurisdictions of the securities to be sold by
the Registering Stockholders, except that the Reorganized Company shall not for
any such purpose be required to qualify generally to do business as a foreign
corporation in any jurisdiction wherein it would not but for the requirements of
this subsection (d) be obligated to be so qualified or to consent to general
service of process in any such jurisdiction;

                           (e) use its best efforts to cause all Registrable
Securities covered by such registration statement to be registered with or
approved by such other federal or state governmental agencies or authorities as
may be necessary in the opinion of counsel to the Reorganized Company and
counsel to the Registering Stockholders to consummate the disposition of such
Registrable Securities;

                           (f) furnish to the Registering Stockholders and each
underwriter, if any, participating in the offering of the securities covered by
such registration statement, a signed counterpart of (i) an opinion of counsel
for the Reorganized Company, and (ii) a "comfort" letter signed by the
independent public accountants who have certified the Reorganized Company's
financial statements included or incorporated by reference in such registration
statement, covering substantially the same matters with respect to such
registration statement (and the prospectus included therein) and, in the case of
the accountants' comfort letter, with respect to events subsequent to the date
of such financial statements, as are customarily covered in opinions of issuer's
counsel and in accountants' comfort letters delivered to the

<PAGE>   10
underwriters in underwritten public offerings of securities (and dated
the dates such opinions and comfort letters are customarily dated) and, in the
case of the legal opinion, such other legal matters, and, in the case of the
accountants' comfort letter, such other financial matters, as the Registering
Stockholders, or the underwriters, may reasonably request;

            (g) promptly notify the Registering Stockholders and each managing
underwriter, if any, participating in the offering of the securities covered by
such registration statement (i) when such registration statement, any
pre-effective amendment, the prospectus or any prospectus supplement related
thereto or post-effective amendment to such registration statement has been
filed, and, with respect to such registration statement or any post-effective
amendment, when the same has become effective; (ii) of any request by the
Commission for amendments or supplements to such registration statement or the
prospectus related thereto or for additional information; (iii) of the issuance
by the Commission of any stop order suspending the effectiveness of such
registration statement or the initiation of any proceedings for that purpose;
(iv) of the receipt by the Reorganized Company of any notification with respect
to the suspension of the qualification of any of the Registrable Securities for
sale under the securities or blue sky laws of any jurisdiction or the initiation
of any proceeding for such purpose; (v) at any time when a prospectus relating
thereto is required to be delivered under the Securities Act, upon discovery
that, or upon 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 any material fact required to be
stated therein or necessary to make the statements therein not misleading, in
the light of the circumstances under which they were made, and in the case of
this clause (v), at the request of the Registering Stockholders promptly prepare
and furnish to the Registering Stockholders and each managing underwriter, if
any, participating in the offering of the Registrable Securities, a reasonable
number of copies of a supplement to or an amendment of such prospectus as may be
necessary so that, as thereafter delivered to the purchasers of such securities,
such prospectus shall not include an untrue statement of a material fact or omit
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 under which
they were made; and (vi) at any time when the representations and warranties of
the Reorganized Company contemplated by Section 2.4(a) or (b) hereof cease to be
true and correct;

            (h) otherwise comply with all applicable rules and regulations of
the Commission, and make available to its security holders, as soon as
reasonably practicable, an earnings statement covering the period of at least
twelve months beginning with the first full calendar month after the effective
date of such registration statement, which earnings statement shall satisfy the
provisions of Section 11(a) of the Securities Act and Rule 158 promulgated
thereunder, and promptly furnish to
<PAGE>   11
the Registering Stockholders a copy of any amendment or supplement to such
registration statement or prospectus;

            (i) provide and cause to be maintained a transfer agent and
registrar (which, in each case, may be the Reorganized Company) for all
Registrable Securities covered by such registration statement from and after a
date not later than the effective date of such registration;

            (j) (i) use its best efforts to cause all Registrable Securities
covered by such registration statement to be listed on the principal securities
exchange on which similar securities issued by the Reorganized Company are then
listed (if any), if the listing of such Registrable Securities is then permitted
under the rules of such exchange, or (ii) if no similar securities are then so
listed, use its best efforts to (x) cause all such Registrable Securities to be
listed on a national securities exchange or (y) failing that, secure designation
of all such Registrable Securities as a NASDAQ "national market system security"
within the meaning of Rule 11Aa2-1 of the Commission or (z) failing that, to
secure NASDAQ authorization for such shares and, without limiting the generality
of the foregoing, to arrange for at least two market makers to register as such
with respect to such shares with the National Association of Securities Dealers,
Inc.;

            (k) deliver promptly to counsel to the Registering Stockholders and
each underwriter, if any, participating in the offering of the Registrable
Securities, copies of all correspondence between the Commission and the
Reorganized Company, its counsel or auditors and all memoranda relating to
discussions with the Commission or its staff with respect to such registration
statement;

            (l) use its best efforts to obtain the withdrawal of any order
suspending the effectiveness of the registration statement;

            (m) provide a CUSIP number for all Registrable Securities, no later
than the effective date of the registration statement; and

            (n) make available its employees and personnel and otherwise provide
reasonable assistance to the underwriters (taking into account the needs of the
Reorganized Company's business) in their marketing of Registrable Securities.

The Reorganized Company may require the Registering Stockholders to furnish the
Reorganized Company such information regarding the Registering Stockholders and
the distribution of the Registrable Securities as the Reorganized Company may
from time to time reasonably request in writing.
<PAGE>   12
      The Stockholders agree that upon receipt of any notice from the
Reorganized Company of the happening of any event of the kind described in
paragraph (g)(iii) or (v) of this Section 2.3, each of the Registering
Stockholders will, to the extent appropriate, discontinue its disposition of
Registrable Securities pursuant to the registration statement relating to such
Registrable Securities until, in the case of paragraph (g)(v) of this Section
2.3, its receipt of the copies of the supplemented or amended prospectus
contemplated by paragraph (g)(v) of this Section 2.3 and, if so directed by the
Reorganized Company, will deliver to the Reorganized Company (at the Reorganized
Company's expense) all copies, other than permanent file copies, then in its
possession, of the prospectus relating to such Registrable Securities current at
the time of receipt of such notice. If the disposition by the Registering
Stockholders of their securities is discontinued pursuant to the foregoing
sentence, the Reorganized Company shall extend the period of effectiveness of
the registration statement by the number of days during the period from and
including the date of the giving of notice to and including the date when the
Registering Stockholders shall have received copies of the supplemented or
amended prospectus contemplated by paragraph (g)(v) of this Section 2.3; and, if
the Reorganized Company shall not so extend such period, the Registering
Stockholders' request pursuant to which such registration statement was filed
shall not be counted for purposes of the requests for registration to which the
Stockholders are entitled pursuant to Section 2.1 hereof.

         2.4 Underwritten Offerings.

            (a) Requested Underwritten Offerings. If requested by the
underwriters for any underwritten offering by the Registering Stockholders (and
any Other Investors) pursuant to a registration requested under Section 2.1, the
Reorganized Company shall enter into a customary underwriting agreement with a
managing underwriter or underwriters selected by the Registering Stockholders.
Such underwriting agreement shall be satisfactory in form and substance to the
Registering Stockholders and shall contain such representations and warranties
by, and such other agreements on the part of, the Reorganized Company and such
other terms as are generally prevailing in agreements of that type, including,
without limitation, customary provisions relating to indemnification and
contribution. The Registering Stockholders shall be parties to such underwriting
agreement and may, at their option, require that any or all of the
representations and warranties by, and the other agreements on the part of, the
Reorganized Company to and for the benefit of such underwriters shall also be
made to and for the benefit of the Registering Stockholders and that any or all
of the conditions precedent to the obligations of such underwriters under such
underwriting agreement be conditions precedent to the obligations of the
Registering Stockholders. None of the Registering Stockholders shall be required
to make any representations or warranties to or agreements with the Reorganized
Company or the underwriters other than representations, warranties or agreements
regarding such Registering Stockholder, its ownership of and title to the
Registrable Securities, and its intended method of
<PAGE>   13
distribution; and any liability of any Registering Stockholder to any
underwriter or other person under such underwriting agreement shall be limited
to liability arising from breach of its representations and warranties and shall
be limited to an amount equal to the proceeds (net of expenses and underwriting
discounts and commissions) that it derives from such registration.

            (b) Incidental Underwritten Offerings. In the case of a registration
pursuant to Section 2.2 hereof, if the Reorganized Company shall have determined
to enter into any underwriting agreements in connection therewith, all of the
Registrable Securities to be included in such registration shall be subject to
such underwriting agreements. The Registering Stockholders may, at their option,
require that any or all of the representations and warranties by, and the other
agreements on the part of, the Reorganized Company to and for the benefit of
such underwriters shall also be made to and for the benefit of the Registering
Stockholders and that any or all of the conditions precedent to the obligations
of such underwriters under such underwriting agreement be conditions precedent
to the obligations of the Registering Stockholders. None of the Registering
Stockholders shall be required to make any representations or warranties to or
agreements with the Reorganized Company or the underwriters other than
representations, warranties or agreements regarding such Registering
Stockholder, its ownership of and title to the Registrable Securities, and its
intended method of distribution; and any liability of any Registering
Stockholder to any underwriter or other Person under such underwriting agreement
shall be limited to liability arising from breach of its representations and
warranties and shall be limited to an amount equal to the proceeds (net of
expenses and underwriting discounts and commissions) that it derives from such
registration.

         2.5 Preparation; Reasonable Investigation. In connection with the
preparation and filing of each registration statement under the Securities Act
pursuant to this Agreement, the Reorganized Company will give the Registering
Stockholders, their underwriters, if any, and their respective counsel,
accountants and other representatives and agents the opportunity to participate
in the preparation of such registration statement, each prospectus included
therein or filed with the Commission, and each amendment thereof or supplement
thereto, and give each of them such access to its books and records and such
opportunities to discuss the business of the Reorganized Company with its
officers and employees and the independent public accountants who have certified
its financial statements, and supply all other information reasonably requested
by each of them, as shall be necessary or appropriate, in the opinion of the
Registering Stockholders and such underwriters' respective counsel, to conduct a
reasonable investigation within the meaning of the Securities Act.

         2.6 Indemnification.

            (a) Indemnification by the Reorganized Company. The Reorganized
Company agrees that in the event of any registration of any securities of the
<PAGE>   14
Reorganized Company under the Securities Act, the Reorganized Company shall, and
hereby does, indemnify and hold harmless each Stockholder, its respective
directors, officers, partners, agents and affiliates and each other Person who
participates as an underwriter in the offering or sale of such securities and
each other Person, if any, who controls such Stockholder or any such underwriter
within the meaning of the Securities Act, against any losses, claims, damages,
or liabilities, joint or several, to which such Stockholder or any such
director, officer, partner, agent or affiliate or underwriter or controlling
person may become subject under the Securities Act or otherwise, insofar as such
losses, claims, damages or liabilities, joint or several (or actions or
proceedings, whether commenced or threatened, in respect thereof), arise out of
or are based upon (i) any untrue statement or alleged untrue statement of any
material fact contained in any registration statement under which such
securities were registered under the Securities Act, any preliminary prospectus,
final prospectus or summary prospectus contained therein, or any amendment or
supplement thereto, (ii) 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
(iii) any violation by the Reorganized Company of any federal, state or common
law rule or regulation applicable to the Reorganized Company and relating to
action required of or inaction by the Reorganized Company in connection with any
such registration, and the Reorganized Company shall reimburse such Stockholder
and each such director, officer, partner, agent or affiliate, underwriter and
controlling Person for any legal or any other expenses reasonably incurred by
them in connection with investigating or defending any such loss, claim,
liability, action or proceeding; provided that the Reorganized Company shall not
be liable in any such case to the Stockholders or any such director, officer,
partner, agent, affiliate, or controlling person to the extent that any such
loss, claim, damage, liability (or action or proceeding in respect thereof) or
expense arises out of or is based upon an untrue statement or alleged untrue
statement or omission or alleged omission made in such registration statement,
any such preliminary prospectus, final prospectus, summary prospectus, amendment
or supplement in reliance upon and in conformity with written information
furnished to the Reorganized Company through an instrument duly executed by or
on behalf of the Stockholders, specifically stating that it is for use in the
preparation thereof; and provided, further, that the Reorganized Company shall
not be liable to any Person who participates as an underwriter in the offering
or sale of Registrable Securities or any other Person, if any, who controls such
underwriter within the meaning of the Securities Act, in any such case to the
extent that any such loss, claim, damage, liability (or action or proceeding in
respect thereof) or expense (i) arises out of or is based upon an untrue
statement or alleged untrue statement or omission or alleged omission made in
such registration statement, any such preliminary prospectus, final prospectus,
summary prospectus, amendment or supplement in reliance upon and in conformity
with written information furnished to the Reorganized Company through an
instrument duly executed by or on behalf of such Person or (ii) arises out of
such Person's failure to send or give a copy of the final prospectus, as the
same may be then supplemented or amended, to the Person asserting an untrue
statement or alleged untrue
<PAGE>   15
statement or omission or alleged omission at or prior to the written
confirmation of the sale of Registrable Securities to such Person if such
statement or omission was corrected in such final prospectus. Such indemnity
shall remain in full force regardless of any investigation made by or on behalf
of any Stockholder or any such director, officer, partner, agent, affiliate,
underwriter or controlling Person and shall survive the transfer of such
securities by such Stockholder.

            (b) Indemnification by the Stockholders. As a condition to including
any Registrable Securities in any registration statement, the Reorganized
Company shall have received an undertaking reasonably satisfactory to it from
each Registering Stockholder so including any Registrable Securities to
indemnify and hold harmless (in the same manner and to the same extent as set
forth in paragraph (a) of this Section 2.6) the Reorganized Company, and each
director of the Reorganized Company, each officer of the Reorganized Company and
each other Person, if any, who controls the Reorganized Company within the
meaning of the Securities Act, with respect to any statement or alleged
statement in or omission or alleged omission from such registration statement,
any preliminary prospectus, final prospectus or summary prospectus contained
therein, or any amendment or supplement thereto, but only to the extent such
statement or alleged statement or omission or alleged omission was made in
reliance upon and in conformity with written information furnished to the
Reorganized Company through an instrument duly executed by such Registering
Stockholder specifically stating that it is for use in the preparation of such
registration statement, preliminary prospectus, final prospectus, summary
prospectus, amendment or supplement; provided, however, that the liability of
such indemnifying party under this Section 2.6(b) shall be limited to the amount
of proceeds (net of expenses and underwriting discounts and commissions)
received by such indemnifying party in the offering giving rise to such
liability. Such indemnity shall remain in full force and effect, regardless of
any investigation made by or on behalf of the Reorganized Company or any such
director, officer or controlling Person and shall survive the transfer of such
securities by such Stockholder.

            (c) Notices of Claims, etc. Promptly after receipt by an indemnified
party of notice of the commencement of any action or proceeding involving a
claim referred to in the preceding subsections of this Section 2.6, such
indemnified party shall, if a claim in respect thereof is to be made against an
indemnifying party, give written notice to the latter of the commencement of
such action or proceeding; provided, however, that the failure of any
indemnified party to give notice as provided herein shall not relieve the
indemnifying party of its obligations under the preceding subsections of this
Section 2.6, except to the extent that the indemnifying party is actually
prejudiced by such failure to give notice, and shall not relieve the
indemnifying party from any liability which it may have to the indemnified party
otherwise than under this Section 2.6. In case any such action or proceeding is
brought against an indemnified party, the indemnifying party shall be entitled
to participate therein and, unless in the opinion of outside counsel to the
indemnified party a conflict of interest between such indemnified and
indemnifying
<PAGE>   16
parties may exist in respect of such claim, to assume the defense thereof,
jointly with any other indemnifying party similarly notified to the extent that
it may wish, with counsel reasonably satisfactory to such indemnified party;
provided, however, that if the defendants in any such action or proceeding
include both the indemnified party and the indemnifying party and if in the
opinion of outside counsel to the indemnified party there may be legal defenses
available to such indemnified party and/or other indemnified parties which are
different from or in addition to those available to the indemnifying party, the
indemnified party or parties shall have the right to select separate counsel to
defend such action or proceeding on behalf of such indemnified party or parties,
provided, however, that the indemnifying party shall be obligated to pay for
only one counsel for all indemnified parties. After notice from the indemnifying
party to such indemnified party of its election so to assume the defense thereof
and approval by the indemnified party of such counsel, the indemnifying party
shall not be liable to such indemnified party for any legal expenses
subsequently incurred by the latter in connection with the defense thereof other
than reasonable costs of investigation (unless the first proviso in the
preceding sentence shall be applicable). No indemnifying party shall be liable
for any settlement of any action or proceeding effected without its written
consent. No indemnifying party shall, without the consent of the 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) Contribution. If the indemnification provided for in this
Section 2.6 shall for any reason be held by a court to be unavailable to an
indemnified party under subsection (a) or (b) hereof in respect of any loss,
claim, damage or liability, or any action in respect thereof, then, in lieu of
the amount paid or payable under subsection (a) or (b) hereof, the indemnified
party and the indemnifying party under subsection (a) or (b) hereof shall
contribute to the aggregate losses, claims, damages and liabilities (including
legal or other expenses reasonably incurred in connection with investigating the
same), (i) in such proportion as is appropriate to reflect the relative fault of
the indemnifying party on the one hand, and the indemnified party on the other,
which resulted in such loss, claim, damage or liability, or action in respect
thereof, with respect to the statements or omissions which resulted in such
loss, claim, damage or liability, or action in respect thereof, as well as any
other relevant equitable considerations, or (ii) if the allocation provided by
clause (i) above is not permitted by applicable law or if the allocation
provided in this clause (ii) provides a greater amount to the indemnified party
than clause (i) above, in such proportion as shall be appropriate to reflect not
only the relative fault but also the relative benefits received by the
indemnifying party and the indemnified party from the offering of the securities
covered by such registration statement as well as any other relevant equitable
considerations. The parties hereto agree that it would not be just and equitable
if contributions pursuant to this Section 2.6(d) were to be determined by pro
rata allocation or by any other method of allocation which does not take into
account the equitable considerations referred to in the
<PAGE>   17
preceding sentence of this Section 2.6(d). No Person guilty of fraudulent
misrepresentation (within the meaning of Section 11(f) of the Securities Act)
shall be entitled to contribution from any Person who was not guilty of such
fraudulent misrepresentation. The Registering Stockholders' obligations to
contribute as provided in this subsection (d) are several and not joint and
shall be in proportion to the relative value of their respective Registrable
Securities covered by such registration statement. In addition, no Person shall
be obligated to contribute hereunder any amounts in payment for any settlement
of any action or claim effected without such Person's consent, which consent
shall not be unreasonably withheld. Notwithstanding anything in this subsection
(d) to the contrary, no indemnifying party (other than the Reorganized Company)
shall be required to contribute any amount in excess of the proceeds (net of
expenses and underwriting discounts and commissions) received by such party from
the sale of the Registrable Securities in the offering to which the losses,
claims, damages or liabilities of the indemnified parties relate.

            (e) Other Indemnification. Indemnification and contribution similar
to that specified in the preceding subsections of this Section 2.6 (with
appropriate modifications) shall be given by the Reorganized Company and the
Registering Stockholders with respect to any required registration or other
qualification of securities under any federal, state or blue sky law or
regulation of any governmental authority other than the Securities Act. The
indemnification agreements contained in this Section 2.6 shall be in addition to
any other rights to indemnification or contribution which any indemnified party
may have pursuant to law or contract and shall remain operative and in full
force and effect regardless of any investigation made by or on behalf of any
indemnified party and shall survive the transfer of any of the Registrable
Securities by any of the Stockholders.

            (f) Indemnification Payments. The indemnification and contribution
required by this Section 2.6 shall be made by periodic payments of the amount
thereof during the course of the investigation or defense, as and when bills are
received or expense, loss, damage or liability is incurred.

         2.7 Unlegended Certificates. In connection with the offering of any
Registrable Securities registered pursuant to this Section 2, the Reorganized
Company shall (i) facilitate the timely preparation and delivery to the
Stockholders, the Other Investors and the underwriters, if any, participating in
such offering, of unlegended certificates representing ownership of such
Registrable Securities being sold in such denominations and registered in such
names as requested by the Stockholders, the Other Investors or such underwriters
and (ii) instruct any transfer agent and registrar of such Registrable
Securities to release any stop transfer orders with respect to any such
Registrable Securities.

         2.8 Limitation on Sale of Securities. The Reorganized Company hereby
agrees that if it shall previously have received a request for registration
pursuant
<PAGE>   18
to Section 2.1 or 2.2 hereof, and if such previous registration shall not have
been withdrawn or abandoned, (i) the Reorganized Company shall not effect any
public or private offer, sale or distribution of its securities or effect any
registration of any of its equity securities under the Securities Act (other
than a registration on Form S-8 or any successor or similar form which is then
in effect), whether or not for sale for its own account, until a period of 90
days (or such shorter period as the Registering Stockholders shall be advised by
their managing underwriter) shall have elapsed from the effective date of such
previous registration, and the Reorganized Company shall so provide in any
registration rights agreements hereafter entered into with respect to any of its
securities; and (ii) the Reorganized Company shall use its best efforts to cause
each holder of its equity securities purchased from the Reorganized Company at
any time after the date of this Agreement to agree not to effect any public sale
or distribution of any such securities during such period, including a sale
pursuant to Rule 144 under the Securities Act.

         2.9 No Required Sale. Nothing in this Agreement shall be deemed to
create an independent obligation on the part of any of the Stockholders to sell
any Registrable Securities pursuant to any effective registration statement.

      3. Rule 144. The Reorganized Company shall take all actions reasonably
necessary to enable holders of Registrable Securities to sell such securities
without registration under the Securities Act within the limitation of the
exemptions provided by (a) Rule 144, or (b) any similar rule or regulation
hereafter adopted by the Commission including, without limiting the generality
of the foregoing, filing on a timely basis all reports required to be filed by
the Exchange Act. Upon the request of a Stockholder, the Reorganized Company
will deliver to such holder a written statement as to whether it has complied
with such requirements.

      4. Amendments and Waivers. This Agreement may be amended, modified or
supplemented only by written agreement of the party against whom enforcement of
such amendment, modification or supplement is sought.

      5. Other Investors. The parties hereto acknowledge and agree that no Other
Investor has any right to request registration of the Common Stock held by such
Other Investor or to participate in any registration of securities by the
Reorganized Company, other than in accordance with the terms of the
stockholder's agreement or option agreement, as the case may be, between such
Other Investor and the Reorganized Company or any of its subsidiaries, pursuant
to which such Other Investor generally may have the right or obligation to
participate in any public offering in which all or a portion of the shares of
Common Stock owned by the Stockholders are registered under the Securities Act.

      6. Adjustments. In the event of any change in the capitalization of the
Reorganized Company as a result of any stock split, stock dividend, reverse
split, combination, recapitalization, merger, consolidation, or otherwise, the
provisions of this
<PAGE>   19
Agreement shall be appropriately adjusted. The Reorganized Company agrees that
it shall not effect or permit to occur any combination or subdivision of shares
which would adversely affect the ability of the Stockholders or the Other
Investors to include any Registrable Securities in any registration contemplated
by this Agreement or the marketability of such Registrable Securities in any
such registration. The Reorganized Company agrees that it will take all
reasonable steps necessary to effect a combination or subdivision of shares if
in the reasonable judgment of the Stockholders such combination or subdivision
would enhance the marketability of the Registrable Securities.

      7. Notice. All notices and other communications hereunder shall be in
writing and, unless otherwise provided herein, shall be deemed to have been
given when received by the party to whom such notice is to be given at its
address set forth below, or such other address for the party as shall be
specified by notice given pursuant hereto:

      (a) If to any of the Stockholders, to it:

          c/o Appaloosa Management, L.P.
          26 Main Street, 1st Floor
          Chatham, New Jersey 07928
          Attention:  James E. Bolin

          With a copy to:

          Fried, Frank, Harris, Shriver
            & Jacobson
          One New York Plaza
          New York, New York 10004
          Attention:  Robert C. Schwenkel, Esq.

      (b) If to the Reorganized Company, to it at:

          Bio-Plexus, Inc.
          129 Reservoir Road
          Vernon, Connecticut 06066
          Attention:  Chief Executive Officer

          With a copy to:

          Reid and Riege, P.C
          One State Street
          Hartford, Connecticut 06103
          Attention:  Craig L. Sylvester, Esq.
<PAGE>   20
      8. Assignment; Third Party Beneficiaries. This Agreement shall be binding
upon and inure to the benefit of and be enforceable by the parties hereto and
their respective successors and permitted assigns; provided, however, that the
Other Investors shall have no rights under this Agreement. This Agreement may
not be assigned by the Reorganized Company, without the prior written consent of
the Stockholders. Any Stockholder may, at its election, at any time or from time
to time, assign its rights under this Agreement, in whole or in part, to any
purchaser of shares of Common Stock held by it.

      9. Remedies. The parties hereto agree that money damages or other remedy
at law would not be sufficient or adequate remedy for any breach or violation
of, or a default under, this Agreement by them and that, in addition to all
other remedies available to them, each of them shall be entitled to an
injunction restraining such breach, violation or default or threatened breach,
violation or default and to any other equitable relief, including without
limitation specific performance, without bond or other security being required.
In any action or proceeding brought to enforce any provision of this Agreement
(including the indemnification provisions thereof), the successful party shall
be entitled to recover reasonable attorneys' fees in addition to its costs and
expenses and any other available remedy.

      10. No Inconsistent Agreements. The Reorganized Company will not, on or
after the date of this Agreement, enter into any agreement with respect to its
securities which is inconsistent with the rights granted to the Stockholders in
this Agreement or otherwise conflicts with the provisions hereof. The
Reorganized Company has not previously entered into any agreement with respect
to its securities granting any registration rights to any Person. The rights
granted to the Stockholders hereunder do not in any way conflict with and are
not inconsistent with any other agreements to which the Reorganized Company is a
party or by which it is bound. The Reorganized Company further agrees that if
any other registration rights agreement entered into after the date of this
Agreement with respect to any of its securities contains terms which are more
favorable to, or less restrictive on, the other party thereto than the terms and
conditions contained in this Agreement are (insofar as they are applicable) with
respect to the Stockholders, then the terms and conditions of this Agreement
shall immediately be deemed to have been amended without further action by the
Reorganized Company or the Stockholders so that the Stockholders shall be
entitled to the benefit of any such more favorable or less restrictive terms or
conditions.

      11. Descriptive Headings. The descriptive headings of the several sections
and paragraphs of this Agreement are inserted for reference only and shall not
control or otherwise affect the meaning hereof.

      12. Governing Law. This Agreement shall be construed and enforced in
accordance with, and the rights and obligations of the parties hereto shall be
governed by, the laws of the State of New York, without giving effect to the
conflicts of law principles
<PAGE>   21
thereof. Each of the parties hereto hereby irrevocably and unconditionally
consents to submit to the exclusive jurisdiction of the courts of the State of
New York and the United States of America located in the County of New York for
any action or proceeding arising out of or relating to this Agreement and the
transactions contemplated hereby (and agrees not to commence any action or
proceeding relating thereto except in such courts), and further agrees that
service of any process, summons, notice or document by U.S. registered mail to
its respective address set forth in Section 7 hereof shall be effective service
of process for any action or proceeding brought against it in any such court.
Each of the parties hereto hereby irrevocably and unconditionally waives any
objection to the laying of venue of any action or proceeding arising out of this
Agreement or the transactions contemplated hereby in the courts of the State of
New York or the United States of America located in the County of New York, and
hereby further irrevocably and unconditionally waives and agrees not to plead or
claim in any such court that any such action or proceeding brought in any such
court has been brought in an inconvenient forum.

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

      14. Invalidity of Provision. The invalidity or unenforceability of any
provision of this Agreement in any jurisdiction shall not affect the validity or
enforceability of the remainder of this Agreement in that jurisdiction or the
validity or enforceability of this Agreement, including that provision, in any
other jurisdiction. If any restriction or provision of this Agreement is held
unreasonable, unlawful or unenforceable in any respect, such restriction or
provision shall be interpreted, revised or applied in a manner that renders it
lawful and enforceable to the fullest extent possible under law.

      15. Further Assurances. Each party hereto shall do and perform or cause to
be done and performed all further acts and things and shall execute and deliver
all other agreements, certificates, instruments, and documents as any other
party hereto reasonably may request in order to carry out the intent and
accomplish the purposes of this Agreement and the consummation of the
transactions contemplated hereby.

      16. Entire Agreement; Effectiveness. This Agreement constitutes the entire
agreement, and supersedes all prior agreements and understandings, oral and
written, between the parties hereto with respect to the subject matter hereof.
<PAGE>   22
      IN WITNESS WHEREOF, the parties have caused this Agreement to be executed
and delivered by their respective officers thereunto duly authorized.


      IN WITNESS WHEREOF, the parties have caused this Agreement to be executed
and delivered by their respective officers thereunto duly authorized.

                            BIO-PLEXUS, INC.

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


                            APPALOOSA INVESTMENT LIMITED
                                PARTNERSHIP I

                            By: Appaloosa Management L.P., its General Partner

                            By: Appaloosa Partners Inc., its General Partner

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


                            PALOMINO FUND LTD.

                            By: Appaloosa Management L.P., its Investment
                                Adviser

                            By: Appaloosa Partners, Inc., its General Partner

                            By:
                                ------------------------------------------------
                                Name:
                                Title:
<PAGE>   23
                                                                       Exhibit A


             STOCKHOLDERS

Appaloosa Investment Limited Partnership I

Palomino Fund Ltd.