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                                                                    EXHIBIT 1.2


                               NOVOSTE CORPORATION
                     SELLING STOCKHOLDER'S POWER OF ATTORNEY
                              AND CUSTODY AGREEMENT


Novoste Corporation
4350-C International Boulevard
Norcross, GA 30093

Novoste Corporation
4350-C International Boulevard
Norcross, GA 30093

Ladies and Gentlemen:

         The undersigned understands that Novoste Corporation (the "Company")
will file a Registration Statement on Form S-3 (the "Registration Statement")
pursuant to the Securities Act of 1933, as amended (the "Securities Act"), in
connection with the proposed sale by the undersigned, the Company and certain
other stockholders of the Company (such holders, including the undersigned,
hereinafter referred to as the "Selling Stockholders") of shares of Common Stock
of the Company ("Common Stock") to certain underwriters (the "Underwriters")
represented by Piper Jaffray, Inc., Cowen & Company and Montgomery Securities
(the "Representatives"), who propose to offer such Common Stock to the public
(the "Offering"). The Company, Selling Stockholders and the Underwriters propose
to enter into a Purchase Agreement in connection with the Offering,
substantially in the form to be filed as an exhibit to the Registration
Statement (the "Purchase Agreement").

         The shares of Common Stock the undersigned desires to sell (the
"Underwritten Shares") are set forth in Schedule I hereto ("Schedule I") and
either are: (i) - issued and outstanding shares of Common Stock held of record
by, and in the name of the undersigned; (ii) - shares of Common Stock issuable
upon exercise of outstanding options or warrants; or (iii) - a combination
thereof.


         Concurrently with the execution and delivery of this Power of Attorney
and Custody Agreement, the undersigned is delivering to Novoste Corporation, as
custodian (the "Custodian") fully endorsed certificates and/or original stock
option and/or warrant agreement(s) with notice(s) of exercise for at least the
number of Underwritten Shares specified in Schedule I (except where such
certificates, and/or agreements and notice(s) previously have been delivered),
pursuant to the terms hereof.
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         I. APPOINTMENT AND POWERS OF ATTORNEYS-IN-FACT.

         1. In connection with the foregoing, the undersigned hereby makes,
constitutes and appoints ________________ and ________________, and each of them
or their successors or substitutes, the true and lawful attorneys-in-fact of the
undersigned (such persons, or either of them or their successors, hereinafter
referred to individually as an "Attorney-in-Fact" and collectively as the
"Attorneys-in-Fact") with respect to all matters arising in connection with the
sale of Securities by the Selling Stockholders to the Underwriters, including,
but not limited to, the full power and authority, in the name and on behalf of
the undersigned to take any and all of the following actions:

                  a. To sell, assign, transfer and deliver to the Underwriters
         up to the number of Underwritten Shares set forth on Schedule I and
         represented by certificate(s) (in negotiable and deliverable form with
         signatures guaranteed by a bank or trust company or by a member firm of
         the New York, Boston, Midwest, Pacific, Philadelphia or American Stock
         Exchange or accompanied by a duly executed stock power or powers, in
         blank, bearing the signature of the Selling Stockholder so guaranteed)
         and/or original stock option and/or warrant agreements and notices of
         exercise deposited with the Custodian at such purchase price per share
         to be paid by the Underwriters that the Attorneys-in-Fact in the sole
         discretion of either of them shall determine and agree to with the
         Underwriters pursuant to the Purchase Agreement, which purchase price
         shall be the same purchase price per share to be paid by the
         Underwriters to the other Selling Stockholders and to the Company;

                  b. For the purpose of effecting such sale, (i) to execute and
         deliver a Purchase Agreement (which agreement will contain, among other
         things, provision for representations, warranties and covenants by the
         Selling Stockholders) by and among the Company, the Selling
         Stockholders and the Underwriters, substantially in the form attached
         hereto as Exhibit A, with such additions thereto and changes therein as
         the Attorneys-in-Fact in the sole discretion of either of them shall
         determine not to be materially adverse to the Selling Stockholder and
         approve (the "Purchase Agreement"), such approval to be conclusively
         evidenced by the execution and delivery thereof by any of the
         Attorneys-in-Fact and (ii) to carry out and comply with all of the
         terms and conditions of the Purchase Agreement, including the making of
         all representations and agreements provided for in the Purchase
         Agreement to be made by and to exercise all authority vested in the
         Selling Stockholder;

                  c. To endorse, transfer and deliver and/or authorize the
         delivery of certificates for the Underwritten Shares to or on the order
         of the Underwriters or to their nominee or nominees pursuant to the
         Purchase Agreement, and to give such orders and instructions to the
         Custodian as the Attorneys-in-Fact may in the sole discretion of either
         of them determine with respect to: (i) the transfer on the books of the
         Company of the Underwritten Shares to be sold by the undersigned in
         order to effect such sale (including the names and denominations in
         which new certificates for such shares are to be issued); (ii) the
         delivery to or for the account of the Underwriters of the certificates
         for such Underwritten Shares against receipt by the Custodian of the
         purchase price to be paid therefore; (iii) the remittance to the
         undersigned of the proceeds, less any discounts, commissions, fees and
         expenses, all as hereinafter described, from any sale of Underwritten
         Shares by the undersigned to the Underwriters; (iv) the return to the
         undersigned of certificates representing the number of shares, if any,
         of Common Stock received by the Custodian but not sold by the
         undersigned 
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         to the Underwriters; (v) the return to the undersigned of original
         stock option and/or warrant agreements and exercise notices with
         respect to shares not sold by the undersigned to the Underwriters; (vi)
         the receipt of any cash payable in lieu of any fractional shares; and
         (vii) such other matters as shall be necessary or desirable to effect
         the intent and purpose of the foregoing;

                  d. To retain Epstein, Becker & Green, P.C. as legal counsel in
         connection with any and all matters referred to herein (it being
         understood and agreed that Epstein, Becker & Green, P.C. also is acting
         as counsel to the Company);

                  e. To instruct the Custodian as to the number of Underwritten
         Shares to be sold by each Selling Stockholder (it being understood and
         agreed to by the undersigned that the Custodian shall be entitled to
         rely on the instructions from the Attorneys-in-Fact as to the purchase
         price per share and the number of Underwritten Shares to be sold by
         each Selling Stockholder; provided, that, the purchase price per share
         shall be the same price paid by the Underwriters to the other Selling
         Stockholders and the Company);

                  f. To make, execute, acknowledge and deliver all such other
         contracts, powers of attorney, orders, receipts, notices, requests,
         instructions, certificates, letters and other writings, including
         without limitation, a request that the Registration Statement be made
         effective, amendments to the Purchase Agreement, actions to facilitate
         the qualification of the Underwritten Shares under the blue sky or
         securities laws of the jurisdictions in which the Underwriters propose
         to offer the Underwritten Shares, and generally to do all things and to
         take all actions that the Attorneys-in-Fact in the sole discretion of
         either of them may consider necessary or proper in connection with or
         to carry out the sale of the Underwritten Shares to the Underwriters,
         as fully as could the undersigned if personally present and acting;

                  g. To approve on behalf of the undersigned any amendments to
         the Registration Statement or the Prospectus (as hereinafter defined)
         and, if applicable, to advise the Securities and Exchange Commission
         (the "Commission") on behalf of the undersigned that such person is
         aware: (i) that the Commission's staff has made summary, cursory or no
         review of the Registration Statement, as applicable; and (ii) that such
         review or lack thereof may not be relied upon in any degree to indicate
         that the Registration Statement is true, complete or accurate;

                  h. To make, acknowledge, verify and file on behalf of the
         undersigned applications, consents to service of process and such other
         undertakings or reports as may be required by law with state
         commissioners or officers administering state blue sky or securities
         laws; and

                  i. If necessary, to endorse (in blank or otherwise) the
         certificate or certificates representing the Underwritten Shares to be
         sold by the undersigned, or a stock power or powers attached to such
         certificate or certificates.

         2. This Power of Attorney and all authority conferred hereby is granted
and conferred subject to and in consideration of the interests of the Company,
the Underwriters and the other Selling Stockholders who may become parties to
the Purchase Agreement, and, for the purposes of 
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                                       -4-


completing the transactions contemplated by the Purchase Agreement and this
Power of Attorney, this Power of Attorney and all authority conferred hereby
shall be irrevocable and shall not be terminated by any act of the undersigned
or by operation of law, whether by the death or incapacity of the undersigned
(or either or any of them) or by the occurrence of any other event or events
(including, without limiting the foregoing, the death or incapacity of any
executor or trustee or the termination of any trust or estate for which the
undersigned is acting as a fiduciary or fiduciaries or, in the case of a
partnership, limited liability company or corporation, by the dissolution of
such partnership, limited liability company or corporation), and if after the
execution hereof the undersigned (or either or any of them) shall die or become
incapacitated, or if any such trust or estate is terminated, or if any such
partnership, limited liability company or corporation dissolved, or if any other
such event or events occur before the completion of the transactions
contemplated by the Purchase Agreement and this Power of Attorney, the
Attorneys-in-Fact nevertheless shall be authorized and directed to complete all
such transactions as if such death, incapacity or other event or events had not
occurred and regardless of notice thereof.

         Notwithstanding the foregoing, if the Purchase Agreement shall not be
entered into prior to November 30, 1997 or otherwise terminated pursuant to the
provisions thereof, then from and after such date the undersigned shall have the
power to revoke all authority hereby conferred by giving written notice to the
Attorneys-in-Fact and the Custodian that this Power of Attorney has been
terminated. Any such termination shall be subject to all lawful action done or
performed by the Attorneys-in-Fact pursuant to this Power of Attorney prior to
actual receipt of such notice.

         3. Each of the Attorneys-in-Fact shall have full power to make and
substitute any Attorney-in-Fact in his place and stead, and the undersigned
hereby ratifies and confirms all that the Attorneys-in-Fact or substitute or
substitutes shall do by virtue of these presents. All actions hereunder may be
taken by any one of the persons named herein as Attorneys-in-Fact or his
substitute. In the event of the death or incapacity of any Attorneys-in-Fact,
the remaining Attorneys-in-Fact may appoint a substitute therefor. The term
"Attorneys-in-Fact" as used herein shall include their respective substitutes.

         II. CUSTODY AGREEMENT

         1. The Selling Stockholder hereby transmits to the Custodian a
certificate or certificates (the "Certificates") representing Common Stock,
and/or original stock option and/or warrant agreements for the purchase of
Common Stock and notices of exercise therefor of the Company, together with (i)
stock powers from the owners of each of the Certificates with signatures
guaranteed by a bank or trust company or by a member firm of the New York,
Boston, Midwest, Pacific, Philadelphia or American Stock Exchange, representing
not less than the number of shares of Common Stock set forth on Schedule I
hereto, and (ii) additional documentation required to effectuate or confirm
compliance with any of the provisions hereof or of the Purchase Agreement. The
Certificates (x) are to be held by you as Custodian for the account of the
Selling Stockholders, and (y) are to be disposed of by you in accordance with
this Custody Agreement.

         2. The Custodian is hereby authorized and directed to hold the
Certificates in its custody and (i) on or immediately prior to the date on which
the Underwritten Shares are purchased pursuant to the Purchase Agreement (the
"Closing Date"), to cause the number of Underwritten Shares to be transferred on
the books of the Company into such names as the Attorneys-in-Fact shall 
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have instructed the Custodian prior to the Closing Date, and to cause to be
issued, against surrender of the Certificates representing such shares, new
certificates for such shares registered in such names and in such denominations
as Attorneys-in-Fact shall have instructed the Custodian prior to the Closing
Date, and upon the instructions of either Attorney-in-Fact, to deliver such new
certificates to the Representative for the accounts of the several Underwriters
pursuant to the Purchase Agreement, against payment for such shares in such
amount as either Attorney-in-Fact shall certify to the Custodian, and to give
receipt for such payment and to deposit the same to the Custodian's account as
Custodian, and (ii) when instructed by either Attorney-in-Fact to do so, the
Custodian is to remit to each of the Selling Stockholders the amount received by
it as payment for such shares, less any discounts and commissions, applicable
fees and expenses (the "Net Proceeds") which discounts and commissions, fees and
expenses the Custodian is hereby authorized to pay for the account of the
Selling Stockholders.

         3. As instructed by either Attorney-in-Fact promptly after the Closing
Date, the Custodian shall return to each of the Selling Stockholders the Net
Proceeds and certificates and/or stock option and/or warrant agreements and
notices of exercise representing the number of Underwritten Shares of such
Selling Stockholder's Common Stock (if any) held by the Custodian that are in
excess of the number of Underwritten Shares sold by such Selling Stockholder
pursuant to the Purchase Agreement.

         4. If the Purchase Agreement shall not be entered into on behalf of the
Selling Stockholders prior to November 30, 1997 or shall be terminated pursuant
to the provisions thereof, then, unless the Custodian shall receive instructions
to the contrary from the Attorney-in-Fact, on or after that date the Custodian
is to return to the undersigned the Certificates deposited with the Custodian,
together with the stock powers delivered therewith.

         5. The authority granted to and conferred on the Custodian hereunder is
subject to and in consideration of the interest of the Company, the Underwriters
and the other Selling Stockholders who may become parties to the Purchase
Agreement. Accordingly, the authority granted hereunder and thereunder is an
agency coupled with an interest and is irrevocable and not subject to
termination by operation of law, whether by death or incapacity, by the
dissolution or liquidation of any corporation, limited liability company or
partnership, or by the occurrence of any other event or events (including,
without limiting the foregoing, the termination of any trust or estate for which
one or more of the Selling Stockholders is or are acting as a fiduciary or
fiduciaries). The Certificates deposited with the Custodian and this Power of
Attorney and Custody Agreement and the Custodian's authority hereunder, are
subject to such interest, and this Power of Attorney and Custody Agreement and
the Custodian's authority hereunder are similarly irrevocable by the undersigned
or any Selling Stockholder and shall not be subject to termination in any such
event. Notwithstanding the death or incapacity of any Selling Stockholder, the
dissolution or liquidation of any Selling Stockholder or any such other event or
events, the Custodian is nevertheless authorized and directed to deal with the
Certificates deposited hereunder in accordance with the terms and conditions
hereof, as if such death, incapacity, dissolution, liquidation or other event or
events had not occurred, regardless of whether or not the Custodian shall have
received notice of such death, incapacity, dissolution, liquidation or other
event or events.

         6. Until the purchase price for the shares of Common Stock sold by each
of the Selling Stockholders pursuant to the Purchase Agreement has been paid to
the Custodian by or for the 
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account of the Underwriters, such Selling Stockholder shall remain the owner of
such shares as are outstanding and shall have the right to vote such shares and
all other outstanding shares (if any) represented by the Certificates deposited
with the Custodian and to receive all dividends and distributions thereon.

         III. REPRESENTATIONS, WARRANTIES AND AGREEMENTS OF SELLING STOCKHOLDER.

         The undersigned Selling Stockholder hereby represents, warrants to and
agrees with the Attorneys-in-Fact, the Company and the Underwriters that:

         1. The undersigned now has and on the Closing Date (as defined in the
Purchase Agreement), and on any later date on which Option Shares (as defined in
the Purchase Agreement) are purchased, will have valid, marketable title to the
Underwritten Shares free and clear of any pledge, lien, security interest,
encumbrance, claim or equitable interest other than pursuant to the Purchase
Agreement; the undersigned has full right, power and authority to sell, assign,
transfer and deliver the Underwritten Shares pursuant to the Purchase Agreement;
and upon delivery of such Underwritten Shares and payment of the purchase price
as therein contemplated, each of the Underwriters will obtain valid, marketable
title to the Underwritten Shares purchased by it free and clear of any security
interest, mortgage, pledge, lien, charge, claim, equity or encumbrance of any
kind, including any liability for estate or inheritance taxes, or any liability
to or claims of any creditor, devisee, legatee or beneficiary of the
undersigned;

         2. The undersigned has duly authorized (if applicable), executed and
delivered, in the form heretofore furnished to the Representatives, a Power of
Attorney and Custody Agreement appointing ________________ and ________________
as Attorneys-in-Fact and the Company as the Custodian; the Power of Attorney and
Custody Agreement constitutes a valid and binding agreement of the undersigned,
enforceable in accordance with its terms, except as the enforcement thereof may
be limited by bankruptcy, insolvency, reorganization, moratorium or other
similar laws relating to or affecting creditors' rights generally or by general
equitable principles; and each of the undersigned's Attorneys-in-Fact, acting
alone, is authorized to execute and deliver the Purchase Agreement and
certificate referred to thereunder on behalf of the undersigned, to determine,
subject to Article I, Section 1(e) hereof, the purchase price to be paid by the
several Underwriters to the undersigned as provided in Section 3 of the Purchase
Agreement, to authorize the delivery of the Underwritten Shares under the
Purchase Agreement and to duly endorse (in blank or otherwise) the certificate
or certificates representing such Underwritten Shares or a stock power or powers
with respect thereto, to accept payment therefor, and otherwise to act on behalf
of the undersigned in connection with the Purchase Agreement. Certificates in
negotiable form for all Underwritten Shares, together with a stock power or
powers duly endorsed in blank by the undersigned, have been placed in custody
with the Custodian for the purpose of effecting delivery pursuant to the
Purchase Agreement;

         3. All authorizations, approvals, consents and orders necessary for the
execution and delivery by the undersigned of the Power of Attorney and Custody
Agreement, the execution and delivery by or on behalf of the undersigned of the
Purchase Agreement and the sale and delivery of the Underwritten Shares under
the Purchase Agreement (other than, at the time of the execution hereof if the
Registration Statement has not yet been declared effective by the Commission,
the issuance of the order of the Commission declaring the Registration Statement
effective and such 
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                                       -7-


authorizations, approvals or consents as may be necessary under state or other
securities or Blue Sky laws) have been obtained and are in full force and
effect; the undersigned, if other than a natural person, has been duly organized
and is validly existing and in good standing under the laws of the jurisdiction
of its organization as the type of entity that it purports to be; and the
undersigned has full right, power and authority to enter into and perform its
obligations under the Purchase Agreement and the Power of Attorney and Custody
Agreement, and to sell, assign, transfer and deliver the Underwritten Shares
pursuant to the Purchase Agreement;

         4. The Purchase Agreement when executed by either Attorney-in-Fact on
behalf of the undersigned will be duly authorized by the undersigned if the
undersigned is not a natural person and will have been duly executed and
delivered by or on behalf of the undersigned and is a valid and binding
agreement of the undersigned, enforceable in accordance with its terms, except
as the indemnification and contribution provisions thereunder may be limited by
applicable law and except as the enforcement thereof may be limited by
bankruptcy, insolvency, reorganization, moratorium or other similar laws
relating to or affecting creditors' rights generally or by general equitable
principles; and the performance of the Purchase Agreement and the consummation
of the transactions therein contemplated will not result in a breach of or
default under any material bond, debenture, note or other evidence of
indebtedness, or any material contract, indenture, mortgage, deed of trust, loan
agreement, lease or other agreement or instrument to which the undersigned is a
party or by which the undersigned or any Underwritten Shares may be bound or, to
the best of the undersigned's knowledge, result in any violation of any law,
order, rule, regulation, writ, injunction or decree of any court or governmental
agency or body or, if the undersigned is other than a natural person, result in
any violation of any provisions of the charter, by-laws or other organizational
documents of the undersigned;

         5. The undersigned has not taken and will not take, directly or
indirectly, any action which is designed to or which has constituted or which
might reasonably be expected to cause or result in stabilization or manipulation
of the price of any security of the Company to facilitate the sale or resale of
the Underwritten Shares;

         6. Such Selling Stockholder has not distributed and will not distribute
any prospectus or other offering material in connection with the offering and
sale of the Underwritten Shares, other than a preliminary prospectus or a final
prospectus;

         7. All information furnished by the undersigned relating to the
undersigned and the Underwritten Shares that is contained in the representations
and warranties of the undersigned in this Power of Attorney and Custody
Agreement or set forth in the Registration Statement and the Prospectus (as
defined in the Purchase Agreement) is and at the time the Registration Statement
became or becomes, as the case may be, effective and at all times subsequent
thereto up to and on the Closing Date, and on any later date on which Option
Shares are to be purchased, was or will be, true, correct and complete, and does
not, and at the time the Registration Statement became or becomes, as the case
may be, effective and at all times subsequent thereto up to and on the Closing
Date and on any later date on which Option Shares are to be purchased, 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 such information not
misleading;
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         8. The undersigned will review the Prospectus and will comply with all
agreements and satisfy all conditions on its part to be complied with or
satisfied pursuant to the Purchase Agreement on or prior to the Closing Date, or
any later date on which Option Shares are to be purchased, as the case may be,
and will advise one of its Attorneys-in-Fact and Piper Jaffray Inc. prior to the
Closing Date or such later date on which Option Shares are to be purchased, as
the case may be, if any statement to be made on behalf of such Selling
Stockholder in any certificate contemplated by the Purchase Agreement would be
inaccurate if made as of the Closing Date or such later date on which Option
Shares are to be purchased, as the case may be;

         9. The undersigned is not aware (without having conducted any
investigation or inquiry) that any of the representations and warranties of the
Company set forth in Section 2(a) of the Purchase Agreement is untrue or
inaccurate in any material respect;

         10. The undersigned does not have, or has waived prior to the date
hereof, any preemptive right, co-sale right or right of first refusal or other
similar right to purchase any of the shares of Common Stock that are to be sold
by the Company or any of the other Selling Stockholders to the Underwriters
pursuant to the Purchase Agreement; and the undersigned does not own any
warrants, options or similar rights to acquire, and does not have any right or
arrangement to acquire, any capital stock, rights, warrants, options or other
securities from the Company, other than those described in the Registration
Statement and the Prospectus;

         11. The undersigned will pay or cause to be paid, in addition to the
underwriting commission or discount (i) all costs and expenses incident to the
performance of the undersigned's obligations pursuant to the Purchase Agreement
that are not otherwise specifically provided for in this section, including: (x)
any fees and expenses of counsel for the undersigned who is not also counsel to
the Company; and (y) all expenses and taxes incident to the sale and delivery of
the shares by the undersigned to the Underwriters pursuant to the Purchase
Agreement; and (ii) any fees, disbursements, and expenses described in Section 4
of the Purchase Agreement that result from the inclusion of the shares held by
the Selling Stockholder in the shares being registered and sold to the
Underwriters pursuant to the Purchase Agreement, which fees, disbursements and
expenses are determined by resolution of the Board of Directors of the Company
to be attributable solely to that Selling Stockholder alone and not to
constitute a normal cost or expense of the registration and sale of all shares.
The undersigned authorizes the Custodian to withhold and pay from the proceeds
from the sale of Underwritten Shares for the account of the undersigned, upon
instruction from the Attorneys-in-Fact, all of the foregoing expenses,
disbursements and fees;

         12. The undersigned has carefully reviewed the Purchase Agreement
including the proposed form of representations, warranties, statements and
agreements to be made by the undersigned as a Selling Stockholder pursuant
thereto, and including, without limitation, those contained in Section 2(b) of
the Purchase Agreement and the indemnity and contribution agreements contained
in Sections 6 of the Purchase Agreement, and does hereby represent, warrant and
agree that: (i) such representations, warranties, statements and agreements
insofar as they relate to the undersigned are true and correct as of the date
hereof and will be true and correct at all times through the Closing Date and
any later date on which Option Shares are to be purchased under the Purchase
Agreement; and (ii) such agreements, insofar as they relate to the undersigned,
have been complied with as of the date hereof and will be complied with on and
after the Closing Date and any later date on which Option Shares are to be
purchased;
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         13. Upon request of the Attorneys-in-Fact, Epstein, Becker & Green,
P.C. or the Representatives or their counsel, the undersigned, if a partnership,
corporation, limited liability company, custodian, trustee and/or guardian, will
supply the Attorneys-in-Fact with all documentation demonstrating authority of
the undersigned to enter into and be bound by this Power of Attorney and Custody
Agreement (e.g., appropriate corporate resolutions, by-laws and charter
documents; partnership agreements; articles of organization; operating
agreements; trust agreements; etc.);

         14. Upon request of the Attorneys-in-Fact, Epstein, Becker & Green,
P.C., or the Representatives or their counsel, the undersigned will supply the
Underwriters with an opinion of counsel for the undersigned to the effect set
forth in Section 5(d) of the Purchase Agreement; and

         15. The information regarding the Selling Stockholder set forth in
Schedule I to this Power of Attorney and Custody Agreement is true and correct
as of the date hereof and shall be true and correct at all times through the
Closing Date (taking into account any sale of shares to the Underwriters
pursuant to the Purchase Agreement prior to such Closing Date) and through any
later date on which Option Shares are to be purchased;

         16. The representations, warranties and agreements of the undersigned
in this Power of Attorney and Custody Agreement and those of the undersigned
contained in the Purchase Agreement, are made for the benefit of, and may be
relied upon by, the other Selling Stockholders, the Attorneys-in-Fact, the
Company and its counsel, the Underwriters and their Representatives, agents and
counsel and the Custodian.

         17. The Undersigned will furnish to the Representatives a properly
completed and executed United States Treasury Department Form W-9 (or other
applicable form or statement specified by the Treasury Department regulations in
lieu thereof), in order to document the Underwriters' compliance with the
reporting and withholding provisions of the Tax Equity and Fiscal Responsibility
Act of 1982 and the Interest and Dividend Tax Compliance Act of 1983, prior to
the Closing Date.

         IV. GENERAL

         1. The Attorneys-in-Fact and the Custodian shall be entitled to act and
rely upon any statement, request, notice or instruction respecting this Power of
Attorney and Custody Agreement, not only as to the authorization, validity and
effectiveness thereof, but also as to the truth and acceptability of any
information therein contained; provided, however, that any statement or notice
to the Attorneys-in-Fact and the Custodian with respect to the Closing Date
under the Purchase Agreement or with respect to the noneffectiveness or
termination of the Purchase Agreement, or advice that the Purchase Agreement has
not been executed and delivered, shall have been confirmed in writing to the
Attorneys-in-Fact and the Custodian by the Representatives.

         2. It is understood that the Attorneys-in-Fact and the Custodian assume
no responsibility or liability to any person other than to deal with the
Certificates deposited with the Custodian and the proceeds from the sale of
securities represented thereby in accordance with the provisions hereof. The
Attorneys-in-Fact and the Custodian, in their capacities as the Attorneys-in-
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Fact and Custodian make no representations with respect to and shall have no
responsibility for the Registration Statement or the Prospectus nor, except as
herein expressly provided, for any aspect of the offering of Common Stock, and
the Attorneys-in-Fact and the Custodian shall not be liable for any error of
judgment or for any act done or omitted or for any mistake of fact or law except
for his or its own gross negligence or bad faith. Each of the Selling
Stockholders agrees to indemnify the Attorneys-in-Fact and the Custodian for and
to hold the Attorneys-in-Fact and the Custodian harmless against any loss,
liability or expense incurred on his or its part arising out of or in connection
with his or its acting as Attorneys-in-Fact or Custodian under this Power of
Attorney and Custody Agreement, as well as the cost and expenses of defending
against any claim of liability in the premises, and not due to the gross
negligence or bad faith of such Attorneys-in-Fact and Custodian, as the case may
be. The undersigned agrees that the Attorneys-in-Fact and Custodian may consult
with counsel of his or its choice (who may be counsel for the Company) and the
Attorneys-in-Fact and Custodian shall have full and complete authorization and
protection for any action taken or suffered by him or it hereunder in good faith
and in accordance with the opinion of such counsel. It is understood that the
Attorneys-in-Fact may, without breaching any express or implied obligation to
the undersigned hereunder, release, amend or modify any other Power of Attorney
and Custody Agreement granted by any other Selling Stockholder; provided that
such release, amendment or modification would not have an adverse effect on the
undersigned.

         3. In case any provision of this Power of Attorney and Custody
Agreement shall be invalid, illegal or otherwise unenforceable, the validity,
legality and enforceability of the remaining provisions shall in no way be
affected or impaired thereby.

         4. This Power of Attorney and Custody Agreement may be executed in one
or more counterparts, all of which shall be considered one and the same
agreement and shall become effective when one or more counterparts have been
signed by each of the parties hereto and delivered to each of the other parties
hereto. This Power of Attorney and Custody Agreement constitutes the entire
agreement of the parties with respect to the subject matter hereof.

         5. Notices, if any, under this Power of Attorney and Custody Agreement
shall be addressed to the Selling Stockholder at its address set forth in the
share records of the Company, unless the Selling Stockholder shall in writing
request a different address. Notices to the Custodian or the Attorneys-in-Fact
may be addressed to the first address written above.

         6. This Power of Attorney and Custody Agreement shall be binding upon
the Selling Stockholder and his, her or its personal representative, successors
and assigns, as the case may be.

         7. It is understood that the Attorneys-in-Fact and Custodian shall
serve entirely without compensation.

         8. This Power of Attorney and Custody Agreement shall be governed by
the laws of the State of Delaware.


                      [Signature page follows immediately]
   11
                                      -11-


         The undersigned hereby executes the foregoing Power of Attorney and
Custody Agreement.

Dated:_____________________, 1997


                                    Very truly yours,

                                    ___________________________________________*


                                    ___________________________________________*
                                    Signature(s) of Selling Stockholder(s)


                                    ___________________________________________*


                                    ___________________________________________*
Signature(s) guaranteed:**          Name(s) and titles(s) if applicable of
                                      Selling Stockholders
______________________________        (Please print)


______________________________      ___________________________________________*
                                    Number of Shares you propose to sell


* To be signed in exactly the same manner as the certificate(s) are registered.

** The signature(s) must be guaranteed by an eligible guarantor under a
medallion signature guarantee program (including a national bank or trust
company or a member firm of the New York, American, Boston, Midwest, Pacific or
Philadelphia stock exchange).
   12
                                      -12-


                             ACCEPTANCE BY CUSTODIAN



         Novoste Corporation, named as Custodian in the foregoing Power of
Attorney and Custody Agreement, hereby acknowledges receipt of the stock
certificates and/or stock option and/or warrant agreements in the form
hereinabove described and agrees to act in accordance with this Power of
Attorney and Custody Agreement.


                                    NOVOSTE CORPORATION


                                    By:_________________________________________
                                       Name:
                                       Title:
Dated:______________, 1997
   13



                                    EXHIBIT A


                               Purchase Agreement
   14
SCHEDULE I




NAME                                  NUMBER OF FIRM SHARES    NUMBER OF OPTION 
                                           TO BE SOLD          SHARES TO BE SOLD
                                                               
Thomas D. Weldon                             100,000                -- 0 --
Charles E. Larson                            100,000                -- 0 --
Advanced Technology Ventures IV, L.P.        100,000                100,000
Noro-Mosely Partners III, L.P.               100,000                30,000