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                                                                    EXHIBIT 10.5

                          REGISTRATION RIGHTS AGREEMENT

     This REGISTRATION RIGHTS AGREEMENT, dated as of December 19, 2001 (this
"Agreement"), is made by and between Aksys, Ltd., a Delaware corporation, with
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headquarters located at Two Marriott Drive, Lincolnshire, IL 60069 (the
"Company"), and U.S. Bancorp Piper Jaffray Inc. (the "Initial Investor").
 -------                                              ----------------


                                    RECITALS:

     A.   In connection with the Engagement Agreement dated October 5, 2001 by
and between the Initial Investor and the Company (the "Engagement Agreement"),
                                                       --------------------
the Company has agreed, upon the terms and subject to the conditions of the
Engagement Agreement, to issue to the Initial Investor Warrants (the "Warrants")
                                                                      --------
to purchase an aggregate of 159,762 shares of the Company's Common Stock, par
value $0.01 per share (the "Warrant Shares").
                            --------------

     B.   Pursuant to the terms of the Engagement Agreement, the Company has
agreed to provide certain registration rights under the Securities Act and
applicable state securities laws with respect to the Warrant Shares.

     In consideration of the premises and the mutual covenants contained herein
and other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the Company and the Initial Investor hereby agree as
follows:

                                    ARTICLE I

                                   DEFINITIONS

     As used in this Agreement, the following terms have the following meanings:

     1.1  "Registrable Securities" means the Warrant Shares (whether outstanding
           ----------------------
or subject to the Warrants) and any shares of capital stock issued or issuable
from time to time (with any adjustments) in exchange for or otherwise with
respect to the Warrant Shares; provided that Warrant Shares will cease to be
Registrable Securities at such time as they have been sold under a Registration
Statement or pursuant to Rule 144. A holder of Registrable Securities includes
holders of the Warrants or holders of the Warrant Shares.

     1.2  "Registration Period" means the period between June 19, 2002 and the
           -------------------
earliest of (i) the date on which all of the Registrable Securities have been
sold by the holders thereof under a Registration Statement or pursuant to Rule
144 or (ii) the date on which all the Registrable Securities may be immediately
sold by the holders thereof without registration and without restriction as to
the number of Registrable Securities to be sold, pursuant to Rule 144 or
otherwise.

     1.3  "Registration Statement" means a Registration Statement of the Company
           ----------------------
filed under the Securities Act.

                                       1

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     1.4  The terms "register," "registered," and "registration" refer to a
                     --------    ----------        ------------
registration effected by preparing and filing a Registration Statement or
statements in compliance with the Securities Act and pursuant to Rule 415 and
the declaration or ordering of effectiveness of such Registration Statement by
the SEC.

     1.5  "Rule 415" means Rule 415 under the Securities Act, or any successor
           --------
rule providing for offering securities on a continuous basis, and applicable
rules and regulations thereunder.

                                   ARTICLE II

                                  REGISTRATION

     2.1  Demand Registration. If at any time during the Registration Period the
          -------------------
Company shall receive a written request for registration from the holders of a
majority in interest of the Registrable Securities, the Company will give
written notice of such request to all holders of Registrable Securities within
10 days of receipt of such notice. The holders of Registrable Securities shall
have 20 days from the date of mailing of such notice by the Company to request
inclusion in such registration. Within 10 days after the last day of such
twenty-day period, the Company will use its best efforts to have filed with the
SEC a Registration Statement on Form S-3 registering the Registrable Securities
that request to be registered. If Form S-3 is not available at that time, then
the Company will use its best efforts to file a Registration Statement on such
form as is then available to effect a registration of the Registrable Securities
within such 10-day period. The Company is only obligated to effect two
registrations under this Section 2.1. The holders of Registrable Securities
shall not have the right to make an underwritten offering pursuant to a
Registration Statement requested pursuant to this Section 2.1.

     2.2  Effectiveness of the Registration Statements. The Company will use its
          --------------------------------------------
best efforts to cause the Registration Statements contemplated by the previous
Section to be declared effective by the SEC as soon as practicable after filing,
and in any event no later than the 30th day after the filing date (the "Required
                                                                        --------
Effective Date"). However, so long as the Company filed the applicable
--------------
Registration Statement within the time period required by Section 2.1, if the
Registration Statement receives any SEC review, then the Required Effective Date
will be the 100th day after the filing date. The Company's best efforts will
include, but are not be limited to, promptly responding to all comments received
from the staff of the SEC. If the Company receives notification from the SEC
that the Registration Statement will receive no action or review from the SEC,
then the Company will request that the Registration Statement become effective
within five business days after such SEC notification.

     2.3  Piggyback Registrations.
          -----------------------

          (a)  If, at any time prior to the expiration of the Registration
Period, a Registration Statement is not effective with respect to all of the
Registrable Securities and the Company decides to register any of its securities
for its own account or for the account of others, then the Company will promptly
give all holders of Registrable Securties written notice thereof and will use
its best efforts to include in such registration all or any part of the
Registrable Securities requested by the holder thereof to be included therein
(excluding any Registrable Securities previously included in a Registration
Statement). This requirement does not apply to Company registrations on Form S-4
or

                                       2

<PAGE>

S-8 or their equivalents (relating to equity securities to be issued in
connection with an acquisition of any entity or business or equity securities
issuable in connection with stock option or other employee benefit plans) or to
registration statements that would otherwise not permit the registration of
resales of previously issued securities. Each holder of Registrable Securties
must give its request for registration under this paragraph to the Company in
writing within 15 days after receipt from the Company of notice of such pending
registration. If the registration for which the Company gives notice is a public
offering involving an underwriting, the Company will so advise the holders of
Registrable Securties as part of the above described written notice. In that
event, if the managing underwriter(s) of the public offering impose a limitation
on the number of shares of Common Stock that may be included in the Registration
Statement because, in such underwriter(s)' judgment, such limitation would be
necessary to effect an orderly public distribution, then the Company shall
include in such registration (i) first, the securities the Company proposes to
sell, (ii) second, the securities desired to be sold pursuant to such
Registration Statement by the stockholder or stockholders which are requiring
the Company pursuant to a contractual registration right to file such
Registration Statement and (iii) third, the Registrable Securities requested by
the holders thereof to be included in such offering, pro rata among the holders
of such Registrable Securities on the basis of the number of shares requested to
be included by each such holder.

          (b)  No right to registration of Registrable Securities under this
Section 2.3 limits in any way the registration required under Section 2.1 above.
The obligations of the Company under this Section 2.3 expire upon the earliest
of (i) the effectiveness of a Registration Statement filed pursuant to Section
2.1 above with respect to the Registrable Securities or the respective portion
thereof, (ii) after the Company has afforded the opportunity for the holders of
Registrable Securties to exercise registration rights under this Section 2.3 for
two registrations (provided, however, that the holder that has had any
Registrable Securities excluded from any Registration Statement in accordance
with this Section 2.3 may include in any additional Registration Statement filed
by the Company the Registrable Securities so excluded), or (iii) expiration of
the Registration Period.

     2.4  Eligibility to use Form S-3. The Company represents and warrants that,
          ---------------------------
as of the date of this Agreement, it meets the requirements for the use of Form
S-3 for registration of the resale of the Registrable Securities by the holders
thereof.

                                   ARTICLE III

                      ADDITIONAL OBLIGATIONS OF THE COMPANY

     3.1  Continued Effectiveness of Registration Statement. Subject to the
          -------------------------------------------------
limitations set forth in Section 3.5, the Company will use its best efforts to
keep any Registration Statement covering the Registrable Securities effective
under Rule 415 at all times during the Registration Period. In the event that
the number of shares available under a Registration Statement filed pursuant to
this Agreement is insufficient to cover all of the Registrable Securities
originally covered by such Registration Statement, the Company will (if
permitted) amend the Registration Statement or file a new Registration Statement
(on the short form available therefor, if applicable), or both, so as to cover
all of the Registrable Securities originally covered by such Registration
Statement. The Company will file such amendment or new Registration Statement as
soon as practicable, but in no event later than 20 business days after the
necessity therefor arises. The Company will use its best

                                       3

<PAGE>

efforts to cause such amendment or new Registration Statement to become
effective as soon as is practicable after the filing thereof.

     3.2  Accuracy of Registration Statements. Assuming the accuracy of
          -----------------------------------
information furnished by or on behalf of the holders of Registrable Securties,
any Registration Statement (including any amendments or supplements thereto and
prospectuses contained therein) filed by the Company covering Registrable
Securities will not contain any 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, in light of the circumstances in which they were made, not
misleading. The Company will promptly prepare and file with the SEC such
amendments (including post-effective amendments) and supplements to the
Registration Statement and the prospectus used in connection with the
Registration Statement as may be necessary to permit sales pursuant to the
Registration Statement at all times during the Registration Period (but subject
to Section 3.5), and, during such period, will comply with the provisions of the
Securities Act with respect to the disposition of all Registrable Securities of
the Company covered by the Registration Statement until the termination of the
Registration Period, or if earlier, until such time as all of such Registrable
Securities have been disposed of in accordance with the intended methods of
disposition by the seller or sellers thereof as set forth in the Registration
Statement.

     3.3  Furnishing Documentation. The Company will furnish to the holder whose
          ------------------------
Registrable Securities are included in a Registration Statement, or to its legal
counsel, (a) promptly after each document is filed with the SEC, one copy of any
Registration Statement filed pursuant to this Agreement and any amendments
thereto, each preliminary prospectus (if any) and final prospectus and each
amendment or supplement thereto; and (b) a number of copies of a prospectus,
including a preliminary prospectus (if any), and all amendments and supplements
thereto, and such other documents as the holder may reasonably request in order
to facilitate the disposition of its Registrable Securities. The Company will
promptly notify by facsimile each holder whose Registrable Securities are
included in any Registration Statement of the effectiveness of the Registration
Statement and any post-effective amendment.

     3.4  Additional Obligations. The Company will use its best efforts to (a)
          ----------------------
register and qualify the Registrable Securities covered by a Registration
Statement under such other securities or blue sky laws of such jurisdictions as
each holder who holds (or has the right to hold) Registrable Securities being
offered reasonably requests, (b) prepare and file in those jurisdictions any
amendments (including post-effective amendments) and supplements to such
registrations and qualifications as may be necessary to maintain their
effectiveness during the Registration Period, (c) take any other actions
necessary to maintain such registrations and qualifications in effect at all
times during the Registration Period, and (d) take any other actions reasonably
necessary or advisable to qualify the Registrable Securities for sale in such
jurisdictions. Notwithstanding the foregoing, the Company is not required, in
connection with such obligations, to (i) qualify to do business in any
jurisdiction where it would not otherwise be required to qualify but for this
Section 3.4, (ii) subject itself to general taxation in any such jurisdiction,
(iii) file a general consent to service of process in any such jurisdiction,
(iv) provide any undertakings that cause material expense or burden to the
Company, or (v) make any change in its charter or bylaws, which in each case the
Company determines to be contrary to the best interests of the Company and its
stockholders.

                                       4

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     3.5  Suspension of Resale Rights.
          ---------------------------

          (a)  The Company will notify (by telephone and also by facsimile and
reputable overnight courier) each holder of Registrable Securities being sold
pursuant to a Registration Statement of the happening of any event of which the
Company has knowledge as a result of which the prospectus included in the
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, in light of the circumstances under
which they were made, not misleading. The Company will make such notification as
promptly as practicable after the Company becomes aware of the event (but in no
event will the Company disclose to any holder of Registrable Securities the
facts or circumstances regarding the event), will promptly prepare a supplement
or amendment to the Registration Statement to correct such untrue statement or
omission, and will deliver a number of copies of such supplement or amendment to
each holder of Registrable Securities being sold pursuant to such Registration
Statement such copies as such holder may reasonably request.

          (b)  Notwithstanding the obligations under Section 3.5(a), if in the
good faith judgment of the Company, following consultation with legal counsel,
it would be detrimental to the Company and its stockholders for resales of
Registrable Securities to be made pursuant to the Registration Statement due to
(i) the existence of a material development or potential material development
involving the Company which the Company would be obligated to disclose in the
Registration Statement, which disclosure would be premature or otherwise
inadvisable at such time or would have a Material Adverse Effect upon the
Company and its stockholders, or (ii) in the good faith judgment of the Company,
it would adversely affect or require premature disclosure of the filing of a
Company-initiated registration of any class of its equity securities, the
Company will have the right to suspend the use of the Registration Statement for
a period of not more than ninety days, provided, however, that the Company will
                                       --------  -------
use its commercially reasonable efforts to keep the length of any such
suspension to as short a period as is practicable given the then existing
circumstances and may so defer or suspend the use of the Registration Statement
no more than two times in any eighteen-month period, and provided, further,
                                                         --------  -------
that, after deferring or suspending the use of the Registration Statement, the
Company may not again defer or suspend the use of the Registration Statement
until a period of thirty days has elapsed after resumption of the use of the
Registration Statement.

          (c)  Subject to the Company's rights under this Section 3, the Company
will use its best efforts to prevent the issuance of any stop order or other
suspension of effectiveness of a Registration Statement and, if such an order is
issued, will use its best efforts to obtain the withdrawal of such order at the
earliest possible time and the Company will promptly notify each holder of
Registrable Securities being sold (or, in the event of an underwritten offering,
the managing underwriters) of the issuance of such order and the resolution
thereof.

          (d)  Notwithstanding anything to the contrary contained herein, if the
use of the Registration Statement is suspended by the Company, the Company will
promptly give notice of the suspension to all holders of Registable Securites
that are covered by the Registration Statement, and will promptly notify each
such holder as soon as the use of the Registration Statement may be resumed.

                                       5

<PAGE>

     3.6  Review by Selling Shareholders. The Company will permit a single firm
          ------------------------------
of legal counsel, designated by the holders of a majority in interest of the
Registrable Securities being sold pursuant to a Registration Statement, to
review the Registration Statement and all amendments and supplements thereto (as
well as all requests for acceleration or effectiveness thereof) a reasonable
period of time prior to their filing with the SEC, and will not file any
document in a form to which such counsel reasonably objects, unless otherwise
required by law in the opinion of the Company's counsel; provided that the time
periods set forth in Section 2.2 shall be tolled to the extent that such legal
counsel does not deliver its final comments relating to such Registration
Statement to the Company within 3 business days after receipt of such
Registration Statement. The sections of any such Registration Statement
including information with respect to the holders of Registrable Securities,
such holders' beneficial ownership of securities of the Company or such holders'
intended method of disposition of Registrable Securities must conform to the
information provided to the Company by each of such holders.

     3.7  Due Diligence; Confidentiality.
          ------------------------------

          (a)  The Company will make available upon reasonable advance notice
during normal business hours for inspection by any holder of Registrable
Securities being sold pursuant to a Registration Statement and any attorney,
accountant or other agent retained by any such holder (collectively, the
"Inspectors"), all pertinent financial and other records, pertinent corporate
 ----------
documents and properties of the Company (collectively, the "Records"), as
                                                            -------
reasonably necessary to enable the Inspector to exercise its due diligence
responsibility in connection with or related to the contemplated offering. The
Company will cause its officers, directors and employees to supply all
information that any Inspector may reasonably request for purposes of performing
such due diligence.

          (b)  Each Inspector will hold in confidence, use only in connection
with the contemplated offering, and will not make any disclosure (except to a
holder of Registrable Securties) of, all Records and other information that the
Company determines in good faith to be confidential, and of which determination
the Inspectors are so notified, unless (i) the disclosure of such Records is
necessary to avoid or correct a misstatement or omission in any Registration
Statement, (ii) the release of such Records is ordered pursuant to a subpoena or
other order from a court or government body of competent jurisdiction, (iii) the
information in such Records has been made generally available to the public
other than by disclosure in violation of this or any other agreement (to the
knowledge of the relevant Inspector), (iv) the Records or other information was
developed independently by an Inspector without breach of this Agreement, (v)
the information was known to the Inspector before receipt of such information
from the Company, or (vi) the information was disclosed to the Inspector by a
third party not under an obligation of confidentiality. The Company is not
required to disclose any confidential information in the Records to any
Inspector unless and until such Inspector has entered into a confidentiality
agreement (in form and substance satisfactory to the Company) with the Company
with respect thereto, substantially in the form of this Section 3.7. Each holder
of Registrable Securties will, upon learning that disclosure of Records
containing confidential information is sought in or by a court or governmental
body of competent jurisdiction or through other means, give prompt notice to the
Company and allow the Company, at the Company's expense, to undertake
appropriate action to prevent disclosure of, or to obtain a protective order
for, the Records deemed confidential. Nothing herein will be deemed to limit the
ability of a holder of
                                       6

<PAGE>

Registrable Securities to sell Registrable Securities in a manner that is
otherwise consistent with applicable laws and regulations.

          (c)  The Company will hold in confidence, and will not make any
disclosure of, information concerning a holder of Registrable Securities
provided to the Company under this Agreement unless (i) disclosure of such
information is necessary to comply with federal or state securities laws, or any
exchange listing or similar rules and regulations, (ii) the disclosure of such
information is necessary to avoid or correct a misstatement or omission in any
Registration Statement, (iii) the release of such information is ordered
pursuant to a subpoena or other order from a court or governmental body of
competent jurisdiction, (iv) such information has been made generally available
to the public other than by disclosure in violation of this Agreement or any
other agreement, (v) the information was disclosed to the Company by a third
party not under an obligation of confidentiality or (vi) such holder of
Registrable Securities consents to the form and content of any such disclosure.
If the Company learns that disclosure of such information concerning a holder of
Registrable Securities is sought in or by a court or governmental body of
competent jurisdiction or through other means, the Company will give prompt
notice to such holder prior to making such disclosure and allow such holder, at
its expense, to undertake appropriate action to prevent disclosure of, or to
obtain a protective order for, such information.

     3.8  Listing. The Company will use best efforts to (i) cause all of the
          -------
Registrable Securities covered by each Registration Statement to be listed on
each national securities exchange on which securities of the same class or
series issued by the Company are then listed, if any, if the listing of such
Registrable Securities is then permitted under the rules of such exchange, or
(ii) to the extent the securities of the same class or series are not then
listed on a national securities exchange, secure the designation and quotation
of all of the Registrable Securities covered by each Registration Statement on
Nasdaq.

     3.9  Share Certificates. The Company will cooperate with the holders of
          ------------------
Registrable Securities being sold to facilitate the timely preparation and
delivery of certificates (not bearing any restrictive legends) representing
Registrable Securities to be offered pursuant to a Registration Statement and
will enable such certificates to be in such denominations or amounts as the case
may be, and registered in such names as the holders of Registrable Securities
may reasonably request.

     3.10 Plan of Distribution. At the request of the holders of a majority in
          --------------------
interest of the Registrable Securities registered pursuant to a Registration
Statement, the Company will promptly prepare and file with the SEC such
amendments (including post-effective amendments) and supplements to the
Registration Statement, and the prospectus used in connection with the
Registration Statement, as may be necessary in order to change the plan of
distribution set forth in such Registration Statement.

     3.11 Securities Laws Compliance. The Company will comply with all
          --------------------------
applicable laws related to any Registration Statement relating to the sale of
Registrable Securities and to offering and sale of securities and with all
applicable rules and regulations of governmental authorities in connection
therewith (including, without limitation, the Securities Act, the Exchange Act
and the rules and regulations promulgated by the SEC).

                                       7

<PAGE>

     3.12 Further Assurances. The Company will take all other reasonable actions
          ------------------
as any holder of Registrable Securities or the underwriters, if any, may
reasonably request to expedite and facilitate disposition by such holder of the
Registrable Securities pursuant to the Registration Statement.

                                   ARTICLE IV

              OBLIGATIONS OF THE HOLDERS OF REGISTRABLE SECURITIES

     4.1  Holder Information. As a condition to the obligations of the Company
          ------------------
to complete any registration pursuant to this Agreement with respect to the
Registrable Securities of each holder thereof, such holder will furnish to the
Company such information regarding itself, the Registrable Securities held by it
and the intended method of disposition of the Registrable Securities held by it
as is reasonably required by the Company to effect the registration of the
Registrable Securities. At least 10 business days prior to the first anticipated
filing date of a Registration Statement for any registration under this
Agreement, the Company will notify each holder of Registrable Securities of the
information the Company requires from that holder if such holder elects to have
any of its Registrable Securities included in the Registration Statement. If,
within three business days prior to the filing date, the Company has not
received the requested information from a holder of Registrable Securities, then
the Company may file the Registration Statement without including Registrable
Securities of that holder.

     4.2  Further Assurances. Each holder of Registrable Securities for which
          ------------------
registration has been requested in accordance with the terms of this Agreement
will cooperate with the Company, as reasonably requested by the Company, in
connection with the preparation and filing of any Registration Statement
hereunder.

     4.3  Suspension of Sales. Upon receipt of any notice from the Company under
          -------------------
Section 3.5, each holder of Registrable Securities will immediately discontinue
disposition of Registrable Securities pursuant to the Registration Statement
covering such Registrable Securities until (i) it receives copies of a
supplemented or amended prospectus contemplated by Section 3.5(a) or (ii) the
Company advises such holder of Registrable Securities that a suspension of sales
under Section 3.5(b) has terminated. If so directed by the Company, each holder
of Registrable Securities will deliver to the Company (at the expense of the
Company) or destroy (and deliver to the Company a certificate of destruction)
all copies in such holder's possession (other than a limited number of file
copies) of the prospectus covering such Registrable Securities that is current
at the time of receipt of such notice.

                                    ARTICLE V

                            EXPENSES OF REGISTRATION

     The Company will bear all reasonable expenses, other than underwriting
discounts and commissions, and transfer taxes, if any, incurred in connection
with registrations, filings or qualifications pursuant to Articles II and III of
this Agreement, including, without limitation, all registration, listing and
qualifications fees, printers and accounting fees, the fees and disbursements

                                       8

<PAGE>

of counsel for the Company, and the reasonable fees and disbursements of one
firm of legal counsel selected pursuant to Section 3.6 hereof (not to exceed
$5,000).

                                   ARTICLE VI

                                 INDEMNIFICATION

     In the event that any Registrable Securities are included in a Registration
Statement under this Agreement:

     6.1  To the extent permitted by law, the Company will indemnify and hold
harmless each holder of such Registrable Securities, any underwriter (as defined
in the Securities Act) for the holders of Registrable Securities, any directors
or officers of such holders of Registrable Securities or such underwriter and
any person who controls such holders of Registrable Securities or such
underwriter within the meaning of the Securities Act or the Exchange Act (each,
an "Indemnified Person") against any losses, claims, damages, expenses or
    ------------------
liabilities (joint or several) (collectively, and together with actions,
proceedings or inquiries by any regulatory or self-regulatory organization,
whether commenced or threatened in respect thereof, "Claims") to which any of
                                                     ------
them become subject under the Securities Act, the Exchange Act or otherwise,
insofar as such Claims arise out of or are based upon any of the following
statements, omissions or violations in a Registration Statement filed pursuant
to this Agreement, any post-effective amendment thereof or any prospectus
included therein: (a) any untrue statement or alleged untrue statement of a
material fact contained in the Registration Statement or any post-effective
amendment thereof or the omission or alleged omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading, (b) any untrue statement or alleged untrue statement of
a material fact contained in the prospectus related to the Registration
Statement (as it may be amended or supplemented) or the omission or alleged
omission to state therein any material fact necessary to make the statements
made therein, in light of the circumstances under which the statements therein
were made, not misleading, or (c) any violation or alleged violation by the
Company of the Securities Act, the Exchange Act or any other law related to the
Registration Statement, including without limitation any state securities law or
any rule or regulation thereunder (the matters in the foregoing clauses (a)
through (c) being, collectively, "Violations"). Subject to the restrictions set
                                  ----------
forth in Section 6.3 with respect to the number of legal counsel, the Company
will reimburse the holders of Registrable Securities and each such underwriter
or controlling person and each such other Indemnified Person, promptly as such
expenses are incurred and are due and payable, for any legal fees or other
reasonable expenses incurred by them in connection with investigating or
defending any Claim. Notwithstanding anything to the contrary contained herein,
the indemnification agreement contained in this Section 6.1: (i) does not apply
to Claims arising out of or based upon a Violation that occurs in reliance upon
and in conformity with information furnished in writing to the Company by an
Indemnified Person expressly for use in connection with the preparation of the
Registration Statement or any such amendment thereof or supplement thereto, if
such prospectus was timely made available by the Company pursuant to Section 3.3
hereof; (ii) does not apply to a Claim arising out of or based on any failure by
any Indemnified Person to comply with prospectus delivery requirements (or the
Securities Act, the Exchange Act or any other law or legal requirement
applicable to them) or any covenant or agreement contained in this Agreement;
and (iii) does not apply to amounts paid in settlement of any Claim if such
settlement is made without the prior written

                                       9

<PAGE>

consent of the Company, which consent will not be unreasonably withheld. This
indemnity obligation will remain in full force and effect regardless of any
investigation made by or on behalf of the Indemnified Persons and will survive
the transfer of the Registrable Securities by the Initial Investor under Article
IX of this Agreement.

     6.2  In connection with any Registration Statement in which a holder of
Registrable Securities is participating, each such participating holder will
indemnify and hold harmless, severally and not jointly, to the same extent and
in the same manner set forth in Section 6.1 above, the Company, each of its
directors, each of its officers who signs the Registration Statement, each
person, if any, who controls the Company within the meaning of the Securities
Act or the Exchange Act, and any other stockholder selling securities pursuant
to the Registration Statement and any of its directors and officers and any
person who controls such stockholder within the meaning of the Securities Act or
the Exchange Act (each an "Indemnified Person") against any Claim to which any
                           ------------------
of them may become subject under the Securities Act, the Exchange Act or
otherwise, insofar as such Claim arises out of or is based upon any of the
following: (a) any matter of the type referred to clause (a) or (b) in Section
6.1 above in each case to the extent (and only to the extent) that such
violation occurs in reliance upon and in conformity with written information
furnished to the Company by such holder of Registrable Securities expressly for
use in connection with such Registration Statement or (b) any failure by such
holder of Registrable Securities to comply with prospectus delivery requirements
(or the Securities Act, the Exchange Act or any other law or legal requirement
applicable to sales under the Registration Statement) or any covenant or
agreement contained in this Agreement with respect to sales under the
Registration Statement. Subject to the restrictions set forth in Section 6.3,
such holder of Registrable Securities will promptly reimburse any legal or other
expenses (promptly as such expenses are incurred and due and payable) reasonably
incurred by them in connection with investigating or defending any such Claim.
However, the indemnity agreement contained in this Section 6.2 does not apply to
amounts paid in settlement of any Claim if such settlement is effected without
the prior written consent of such holder of Registrable Securities, which
consent will not be unreasonably withheld, and no holder of Registrable
Securities will be liable under this Agreement (including this Section 6.2 and
Article VII) for the amount of any Claim that exceeds the net proceeds actually
received by such holder of Registrable Securities as a result of the sale of
Registrable Securities pursuant to such Registration Statement. This indemnity
will remain in full force and effect regardless of any investigation made by or
on behalf of an Indemnified Party and will survive the transfer of the
Registrable Securities by the Initial Investor under Article IX of this
Agreement.

     6.3  Promptly after receipt by an Indemnified Person under this Article VI
of notice of the commencement of any action (including any governmental action),
such Indemnified Person will, if a Claim in respect thereof is to be made
against any indemnifying party under this Article VI, deliver to the
indemnifying party a written notice of the commencement thereof. The
indemnifying party may participate in, and, to the extent the indemnifying party
so desires, jointly with any other indemnifying party similarly given notice,
assume control of the defense thereof with counsel mutually satisfactory to the
indemnifying parties and the Indemnified Person. In that case, the indemnifying
party will diligently pursue such defense. If, in the reasonable opinion of
counsel retained by the indemnifying party, the representation by such counsel
of the Indemnified Person and the indemnifying party would be inappropriate due
to the

                                       10

<PAGE>

actual or potential conflicts of interest between the Indemnified Person and any
other party represented by such counsel in such proceeding or the actual or
potential defendants in, or targets of, any such action including the
Indemnified Person and such Indemnified Person reasonably determines that there
may be legal defenses available to such Indemnified Person that are different
from or in addition to those available to the indemnifying party, then the
Indemnified Person is entitled to assume such defense and may retain its own
counsel, with the fees and expenses to be paid by the indemnifying party
(subject to the restrictions on settlement under Section 6.1 or 6.2, as
applicable). The Company will pay for only one separate legal counsel for the
holders of Registrable Securities collectively, and such legal counsel will be
selected by the holders of a majority in interest of the Registrable Securities.
The failure to deliver written notice to the indemnifying party within a
reasonable time of the commencement of any such action does not relieve an
indemnifying party of any liability to an Indemnified Person under this Article
VI, except to the extent that the indemnifying party is prejudiced in its
ability to defend such action. The indemnification required by this Article VI
will be made by periodic payments of the amount thereof during the course of the
investigation or defense, as such expense, loss, damage or liability is incurred
and is due and payable.

                                   ARTICLE VII

                                  CONTRIBUTION

     To the extent that any indemnification provided for herein is prohibited or
limited by law, the indemnifying party will make the maximum contribution with
respect to any amounts for which it would otherwise be liable under Article VI
to the fullest extent permitted by law. However, (a) no contribution will be
made under circumstances where the maker would not have been liable for
indemnification under the fault standards set forth in Article VI, (b) no seller
of Registrable Securities guilty of fraudulent misrepresentation (within the
meaning of Section 11(f) of the Securities Act) will be entitled to contribution
from any seller of Registrable Securities who was not guilty of such fraudulent
misrepresentation, and (c) contribution (together with any indemnification or
other obligations under this Agreement) by any seller of Registrable Securities
will be limited in amount to the net amount of proceeds received by such seller
from the sale of such Registrable Securities.

                                  ARTICLE VIII

                             EXCHANGE ACT REPORTING

     In order to make available to the holders of Registrable Securities the
benefits of Rule 144 or any similar rule or regulation of the SEC that may at
any time permit such holders to sell securities of the Company to the public
without registration, the Company will, until the end of the Registration
Period:

          (a)  File with the SEC in a timely manner, and make and keep
available, all reports and other documents required of the Company under the
Securities Act and the Exchange Act so long as the Company remains subject to
such requirements and the filing and availability of such reports and other
documents is required for the applicable provisions of Rule 144; and

          (b)  Furnish to each holder of Registrable Securities, so long as such
holder of Registrable Securities holds Registrable Securities, promptly upon
such holder's request, (i) a written

                                       11

<PAGE>

statement by the Company that it has complied with the reporting requirements of
the Securities Act and the Exchange Act, (ii) a copy of the most recent annual
or quarterly report of the Company and such other reports and documents filed by
the Company with the SEC and (iii) such other information as may be reasonably
requested to permit the holders of Registrable Securities to sell such
securities pursuant to Rule 144 without registration.

                                   ARTICLE IX

                        ASSIGNMENT OF REGISTRATION RIGHTS

     The rights of the Initial Investor hereunder, including the right to have
the Company register Registrable Securities pursuant to this Agreement, will be
automatically assigned by the Initial Investor to transferees or assignees of
all or any portion of the Registrable Securities, but only if (a) the Initial
Investor agrees in writing with the transferee or assignee to assign such
rights, and a copy of such agreement is furnished to the Company within a
reasonable time after such assignment, (b) the Company is, within a reasonable
time after such transfer or assignment, furnished with written notice of the
name and address of such transferee or assignee and the securities with respect
to which such registration rights are being transferred or assigned, (c) such
transfer or assignment was not made under the Registration Statement or Rule
144, (d) at or before the time the Company received the written notice
contemplated by clause (b) of this sentence, the transferee or assignee agrees
in writing with the Company to be bound by all of the provisions contained
herein, (e) such transfer is made in accordance with the applicable requirements
of the Warrants, as the case may be, and (f) the transferee is an "accredited
investor" as that term is defined in Rule 501 of Regulation D. Any transferee or
assignee of the Initial Investor under Article IX shall be deemed the "Initial
Investor" and a "holder of Registrable Securities" for all purposes of this
Agreement, and shall be entitled to all rights of, and subject to all
obligations (including indemnification obligations) of, the Initial Investor and
a holder of Registrable Securities hereunder.

                                    ARTICLE X

                        AMENDMENT OF REGISTRATION RIGHTS

     This Agreement may be amended and the obligations hereunder may be waived
(either generally or in a particular instance, and either retroactively or
prospectively) only with the written consent of the Company and of the holders
then holding a majority in interest of the Registrable Securities (but not
including any such holder who is not affected by such amendment or waiver). Any
amendment or waiver effected in accordance with this Article X is binding upon
each holder of Registrable Securities and the Company. Notwithstanding the
foregoing, no amendment or waiver will retroactively affect any holder of
Registrable Securities without its consent, or will prospectively adversely
affect any former holder of Registrable Securities who no longer owns
Registrable Securities without its consent. Neither Article VI nor Article VII
hereof may be amended or waived in a manner adverse to a holder of Registrable
Securities without its consent.

                                   ARTICLE XI

                                  MISCELLANEOUS


                                     12

<PAGE>

     11.1 Conflicting Instructions. A person or entity is deemed to be a holder
          -------------------------
of Registrable Securities whenever such person or entity owns of record such
Registrable Securities. If the Company receives conflicting instructions,
notices or elections from two or more persons or entities with respect to the
same Registrable Securities, the Company will act upon the basis of
instructions, notice or election received from the registered owner of such
Registrable Securities.

     11.2 Notices. Any notices required or permitted to be given under the terms
          -------
of this Agreement must be sent by certified or registered mail (return receipt
requested) or delivered personally or by courier (including a recognized
overnight delivery service) or by facsimile and will be effective five days
after being placed in the mail, if mailed by regular U.S. mail, or upon receipt,
if delivered personally or by facsimile, in each case addressed to a party. Any
notice sent by courier (including a recognized overnight delivery service) will
be deemed received one business day after being sent. The addresses for such
communications are:

     If to the Company:                 Aksys, Ltd.
                                        Two Marriot Drive
                                        Lincolnshire, IL 60069
                                        Attention: President
                                        (847) 229-2080

     With a copy to:                    Kirkland & Ellis
                                        200 East Randolph Drive
                                        Chicago, IL 60601
                                        Attention: Keith S. Crow
                                        (312) 861-2200

     If to the Intial Investor:         U.S. Bancorp Piper Jaffray
                                        800 Nicollet Mall
                                        Mail Station J1012005
                                        Minneapolis, MN 55402-7020
                                        Attention: Jon Salveson
                                        (612) 303-1036

     With a copy to:                    Faegre & Benson LLP
                                        2200 Wells Fargo Center
                                        90 South Seventh Street
                                        Minneapolis, MN 55402-3901
                                        Attention: David B. Miller
                                        (612) 766-1600

     If to a holder of Registrable Securities other than the Intial Investor: To
the address reflected in the records of the Company.

     Each party will provide written notice to the other parties of any change
in its address.

                                       13

<PAGE>

     11.3  Waiver. Failure of any party to exercise any right or remedy under
           ------
this Agreement or otherwise, or delay by a party in exercising such right or
remedy, does not operate as a waiver thereof.

     11.4  Governing Law. This Agreement will be governed by and interpreted in
           -------------
accordance with the laws of the State of Illinois without regard to the
principles of conflict of laws. The parties hereto hereby submit to the
exclusive jurisdiction of the United States federal and state courts located in
the State of Illinois with respect to any dispute arising under this Agreement,
the agreements entered into in connection herewith or the transactions
contemplated hereby or thereby.

     11.5  Severability. If any provision of this Agreement is invalid or
           ------------
unenforceable under any applicable statute or rule of law, then such provision
will be deemed modified in order to conform with such statute or rule of law.
Any provision hereof that may prove invalid or unenforceable under any law will
not affect the validity or enforceability of any other provision hereof.

     11.6  Entire Agreement. This Agreement and the Warrants (including all
           ----------------
schedules and exhibits thereto) constitute the entire agreement among the
parties hereto with respect to the subject matter hereof and thereof. There are
no restrictions, promises, warranties or undertakings, other than those set
forth or referred to herein or therein. This Agreement supersedes all prior
agreements and understandings among the parties hereto with respect to the
subject matter hereof.

     11.7  Successors and Assigns. Subject to the requirements of Article IX
           ----------------------
hereof, this Agreement inures to the benefit of and is binding upon the
successors and assigns of each of the parties hereto. Notwithstanding anything
to the contrary herein, including, without limitation, Article IX, the rights of
holder of Registrable Securities are assignable to and exercisable by a bona
fide pledgee of the Registrable Securities in connection with such holder's
margin or brokerage accounts.

     11.8  Use of Pronouns. All pronouns refer to the masculine, feminine or
           ---------------
neuter, singular or plural, as the context may require.

     11.9  Headings. The headings of this Agreement are for convenience of
           --------
reference only, are not part of this Agreement and do not affect its
interpretation.

     11.10 Counterparts. This Agreement may be executed in two or more
           ------------
counterparts, each of which is deemed an original but all of which constitute
one and the same agreement. This Agreement, once executed by a party, may be
delivered to the other party hereto by facsimile transmission, and facsimile
signatures are binding on the parties hereto.

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

     11.12 Consents. All consents and other determinations to be made by the
           --------
holders of Registrable Securities pursuant to this Agreement will be made by the
Initial Investor or the holders

                                       14

<PAGE>

of a majority in interest of the Registrable Securities, determined as if all
Warrants then outstanding had been exercised for Registrable Securities.

     11.13 No Strict Construction. The language used in this Agreement is deemed
           ----------------------
to be the language chosen by the parties to express their mutual intent, and no
rules of strict construction will be applied against any party.

                                     * * * *

                                       15

<PAGE>

     IN WITNESS WHEREOF, the undersigned Initial Investor and the Company have
caused this Agreement to be duly executed as of the date first above written.

                                                 COMPANY:

                                                 AKSYS, LTD.


                                                 By:    /s/ William C. Dow
                                                 Name:  William C. Dow
                                                 Title: President & CEO



                                                 INITIAL INVESTOR:

                                                 U.S. BANCORP PIPER JAFFRAY INC.


                                                 By:    /s/ Jon W. Salveson
                                                 Name:  Jon W. Salveson
                                                 Title: Managing Director

                                       16