Document:

EXHIBIT 4.3

THESE SECURITIES HAVE NOT BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE
COMMISSION OR THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN
EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
"SECURITIES ACT"), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT
TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO
AN AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE
REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH
APPLICABLE STATE SECURITIES LAWS AS EVIDENCED BY A LEGAL OPINION OF COUNSEL TO
THE TRANSFEROR TO SUCH EFFECT, THE SUBSTANCE OF WHICH SHALL BE REASONABLY
ACCEPTABLE TO THE COMPANY. THESE SECURITIES MAY BE PLEDGED IN CONNECTION WITH A
BONA FIDE MARGIN ACCOUNT WITH A REGISTERED BROKER-DEALER OR OTHER LOAN WITH A
FINANCIAL INSTITUTION THAT IS AN "ACCREDITED INVESTOR" AS DEFINED IN RULE 501(a)
UNDER THE SECURITIES ACT.

                             STOCK PURCHASE WARRANT

                To Purchase __________ Shares of Common Stock of

                                  AXONYX, INC.

            THIS STOCK PURCHASE WARRANT CERTIFIES that, for value received,
_____________ (the "Holder"), is entitled, upon the terms and subject to the
limitations on exercise and the conditions hereinafter set forth, at any time on
or after January __, 2004 (the "Initial Exercise Date") and on or prior to the
close of business on the five-year anniversary of the Initial Exercise Date (the
"Termination Date") but not thereafter, to subscribe for and purchase from
Axonyx, Inc., a corporation incorporated in the State of Nevada (the "Company"),
up to ____________ shares (the "Warrant Shares") of Common Stock, par value
$0.001 per share, of the Company (the "Common Stock"). The purchase price of one
share of Common Stock (the "Exercise Price") under this Warrant shall be $7.25,
subject to adjustment hereunder. The Exercise Price and the number of Warrant
Shares for which the Warrant is exercisable shall be subject to adjustment as
provided herein. Capitalized terms used and not otherwise defined herein shall
have the meanings set forth in that certain Securities Purchase Agreement (the
"Purchase Agreement"), dated January 8, 2004, between the Company and each
investor signatory thereto.

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<PAGE>

            1. Title to Warrant. Prior to the Termination Date and subject to
compliance with applicable laws and Section 7 of this Warrant, this Warrant and
all rights hereunder are transferable, in whole or in part, at the office or
agency of the Company by the Holder in person or by duly authorized attorney,
upon surrender of this Warrant together with the Assignment Form annexed hereto
properly endorsed. The transferee shall sign an investment letter in form and
substance reasonably satisfactory to the Company.

            2. Authorization of Shares. The Company covenants that all Warrant
Shares which may be issued upon the exercise of the purchase rights represented
by this Warrant will, upon exercise of the purchase rights represented by this
Warrant, be duly authorized, validly issued, fully paid and nonassessable and
free from all taxes, liens and charges in respect of the issue thereof (other
than taxes in respect of any transfer occurring contemporaneously with such
issue).

            3. Exercise of Warrant.

                  (a) Except as provided in Section 4 herein, exercise of the
      purchase rights represented by this Warrant may be made at any time or
      times on or after the Initial Exercise Date and on or before the
      Termination Date by the surrender of this Warrant and the Notice of
      Exercise Form annexed hereto duly executed, at the office of the Company
      (or such other office or agency of the Company as it may designate by
      notice in writing to the registered Holder at the address of such Holder
      appearing on the books of the Company) and upon payment of the Exercise
      Price of the shares thereby purchased by wire transfer or cashier's check
      drawn on a United States bank or by means of a cashless exercise pursuant
      to Section 3(d). Upon such exercise, the Holder shall be entitled to
      receive a certificate for the number of Warrant Shares so purchased.
      Certificates for shares purchased hereunder shall be delivered to the
      Holder within five Trading Days after the date on which this Warrant shall
      have been exercised as aforesaid. Notwithstanding anything herein to the
      contrary, in lieu of issuing certificates for shares purchased hereunder,
      upon mutual agreement of the Company and the Holder, the Company may
      authorize its transfer agent to issue shares through electronic
      transactions. This Warrant shall be deemed to have been exercised and such
      certificate or certificates shall be deemed to have been issued, and
      Holder or any other person so designated to be named therein shall be
      deemed to have become a holder of record of such shares for all purposes,
      as of the date the Warrant has been exercised by payment to the Company of
      the Exercise Price and all taxes required to be paid by the Holder, if
      any, pursuant to Section 5 prior to the issuance of such shares, have been
      paid. If the Company fails to deliver to the Holder a certificate or
      certificates representing the Warrant Shares pursuant to this Section 3(a)
      by the fifth Trading Day after the date of exercise, then the Holder will
      have the right to rescind such exercise.

                  (b) If this Warrant shall have been exercised in part, the
      Company shall, at the time of delivery of the certificate or certificates
      representing Warrant Shares, deliver to Holder a new Warrant evidencing
      the rights of Holder to purchase the

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<PAGE>

      unpurchased Warrant Shares called for by this Warrant, which new Warrant
      shall in all other respects be identical with this Warrant.

                  (c) Notwithstanding anything herein to the contrary, in no
      event shall the Holder be permitted to exercise this Warrant for Warrant
      Shares to the extent that (i) the number of shares of Common Stock
      beneficially owned by such Holder, together with any affiliate thereof
      (other than Warrant Shares issuable upon exercise of this Warrant) plus
      (ii) the number of Warrant Shares issuable upon exercise of this Warrant,
      would be equal to or exceed 4.9999% of the number of shares of Common
      Stock then issued and outstanding, including shares issuable upon exercise
      of this Warrant held by such Holder after application of this Section
      3(c). As used herein, beneficial ownership shall be determined in
      accordance with Section 13(d) of the Exchange Act and the rules
      promulgated thereunder. To the extent that the limitation contained in
      this Section 3(c) applies, the determination of whether this Warrant is
      exercisable (in relation to other securities owned by the Holder) and of
      which a portion of this Warrant is exercisable shall be in the sole
      discretion of such Holder, and the submission of a Notice of Exercise
      shall be deemed to be such Holder's determination of whether this Warrant
      is exercisable (in relation to other securities owned by such Holder) and
      of which portion of this Warrant is exercisable, in each case subject to
      such aggregate percentage limitation, and the Company shall have no
      obligation to verify or confirm the accuracy of such determination.
      Nothing contained herein shall be deemed to restrict the right of a Holder
      to exercise this Warrant into Warrant Shares at such time as such exercise
      will not violate the provisions of this Section 3(c). The provisions of
      this Section 3(c) may be waived by the Holder upon, at the election of the
      Holder, not less than 61 days' prior notice to the Company, and the
      provisions of this Section 3(c) shall continue to apply until such 61st
      day (or such later date, as determined by the Holder, as may be specified
      in such notice of waiver). No exercise of this Warrant in violation of
      this Section 3(c) but otherwise in accordance with this Warrant shall
      affect the status of the Warrant Shares as validly issued, fully-paid and
      nonassessable.

                  (d) If at any time after one year from the date of issuance of
      this Warrant there is no effective Registration Statement registering the
      resale of the Warrant Shares by the Holder at a time when such
      Registration Statement is otherwise required to be effective pursuant to
      the Registration Rights Agreement (and subject to any suspension or
      blackout periods provided for therein), this Warrant may also be exercised
      at such time by means of a "cashless exercise" in which the Holder shall
      be entitled to receive a certificate for the number of Warrant Shares
      equal to the quotient obtained by dividing [(A-B) (X)] by (A), where:

            (A) = the Closing Price on the Trading Day immediately preceding
                  the date of such election;

            (B) = the Exercise Price of the Warrants, as adjusted; and

            (X) = the number of Warrant Shares issuable upon exercise of the
                  Warrants in accordance with the terms of this Warrant.

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<PAGE>

            4. No Fractional Shares or Scrip. No fractional shares or scrip
representing fractional shares shall be issued upon the exercise of this
Warrant. As to any fraction of a share which Holder would otherwise be entitled
to purchase upon such exercise, the Company shall pay a cash adjustment in
respect of such final fraction in an amount equal to such fraction multiplied by
the Exercise Price.

            5. Charges, Taxes and Expenses. Issuance of certificates for Warrant
Shares shall be made without charge to the Holder for any issue or transfer tax
or other incidental expense in respect of the issuance of such certificate, all
of which taxes and expenses shall be paid by the Company, and such certificates
shall be issued in the name of the Holder or in such name or names as may be
directed by the Holder; provided, however, that in the event certificates for
Warrant Shares are to be issued in a name other than the name of the Holder,
this Warrant when surrendered for exercise shall be accompanied by the
Assignment Form attached hereto duly executed by the Holder; and the Company may
require, as a condition thereto, the payment of a sum sufficient to reimburse it
for any transfer tax incidental thereto.

            6. Closing of Books. The Company will not close its stockholder
books or records in any manner which prevents the timely exercise of this
Warrant, pursuant to the terms hereof.

            7. Transfer, Division and Combination.

                  (a) Subject to compliance with any applicable securities laws
      and the conditions set forth in Sections 1 and 7(f) hereof and to the
      provisions of Section 4.1 of the Purchase Agreement, this Warrant and all
      rights hereunder are transferable, in whole or in part, upon surrender of
      this Warrant at the principal office of the Company, together with a
      written assignment of this Warrant substantially in the form attached
      hereto duly executed by the Holder or its agent or attorney and funds
      sufficient to pay any transfer taxes payable upon the making of such
      transfer. Upon such surrender and, if required, such payment, the Company
      shall execute and deliver a new Warrant or Warrants in the name of the
      assignee or assignees and in the denomination or denominations specified
      in such instrument of assignment, and shall issue to the assignor a new
      Warrant evidencing the portion of this Warrant not so assigned, and this
      Warrant shall promptly be cancelled. A Warrant, if properly assigned, may
      be exercised by a new holder for the purchase of Warrant Shares without
      having a new Warrant issued.

                  (b) This Warrant may be divided or combined with other
      Warrants of like tenor and terms upon presentation hereof at the aforesaid
      office of the Company, together with a written notice specifying the names
      and denominations in which new Warrants are to be issued, signed by the
      Holder or its agent or attorney. Subject to compliance with Section 7(a),
      as to any transfer which may be involved in such division or combination,
      the Company shall execute and deliver a new Warrant or Warrants in
      exchange for the Warrant or Warrants to be divided or combined in
      accordance with such notice.

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<PAGE>

                  (c) The Company shall prepare, issue and deliver at its own
      expense (other than transfer taxes) the new Warrant or Warrants under this
      Section 7.

                  (d) The Company agrees to maintain, at its aforesaid office,
      books for the registration and the registration of transfer of the
      Warrants.

                  (e) If, at the time of the surrender of this Warrant in
      connection with any transfer of this Warrant, the transfer of this Warrant
      shall not be registered pursuant to an effective registration statement
      under the Securities Act and under applicable state securities or blue sky
      laws, the Company may require, as a condition of allowing such transfer
      (i) that the Holder or transferee of this Warrant, as the case may be,
      furnish to the Company a written opinion of counsel (which opinion shall
      be in form, substance and scope customary for opinions of counsel in
      comparable transactions) to the effect that such transfer may be made
      without registration under the Securities Act and under applicable state
      securities or blue sky laws, (ii) that the holder or transferee execute
      and deliver to the Company an investment letter in form and substance
      acceptable to the Company and (iii) that the transferee be an "accredited
      investor" as defined in Rule 501(a) promulgated under the Securities Act.

            8. No Rights as Shareholder until Exercise. This Warrant does not
entitle the Holder to any voting rights or other rights as a shareholder of the
Company prior to the exercise hereof. Upon the surrender of this Warrant and the
payment of the aggregate Exercise Price (or by means of a cashless exercise, if
applicable), the Warrant Shares so purchased shall be and be deemed to be issued
to such Holder as the record owner of such shares as of the close of business on
the later of the date of such surrender or payment.

            9. Loss, Theft, Destruction or Mutilation of Warrant. The Company
covenants that upon receipt by the Company of evidence reasonably satisfactory
to it of the loss, theft, destruction or mutilation of this Warrant or any stock
certificate relating to the Warrant Shares, and in case of loss, theft or
destruction, of indemnity or security reasonably satisfactory to it (which, in
the case of the Warrant, shall not include the posting of any bond), and upon
surrender and cancellation of such Warrant or stock certificate, if mutilated,
the Company will make and deliver a new Warrant or stock certificate of like
tenor and dated as of such cancellation, in lieu of such Warrant or stock
certificate.

            10. Saturdays, Sundays, Holidays, etc. If the last or appointed day
for the taking of any action or the expiration of any right required or granted
herein shall be a Saturday, Sunday or a legal holiday, then such action may be
taken or such right may be exercised on the next succeeding day not a Saturday,
Sunday or legal holiday.

            11. Adjustments of Exercise Price and Number of Warrant Shares;
Stock Splits, etc. The number and kind of securities purchasable upon the
exercise of this Warrant and the Exercise Price shall be subject to adjustment
from time to time upon the happening of any of the following. In case the
Company shall (i) pay a dividend in shares of Common Stock or make a
distribution in shares of Common Stock to holders of its outstanding Common
Stock, (ii) subdivide its outstanding shares of Common Stock into a greater
number of shares, (iii) combine its outstanding shares of Common Stock into a
smaller number of shares of Common Stock, or

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<PAGE>

(iv) issue any shares of its capital stock in a reclassification of the Common
Stock, then the number of Warrant Shares purchasable upon exercise of this
Warrant immediately prior thereto shall be adjusted so that the Holder shall be
entitled to receive the kind and number of Warrant Shares or other securities of
the Company which it would have owned or have been entitled to receive had such
Warrant been exercised in advance thereof. Upon each such adjustment of the kind
and number of Warrant Shares or other securities of the Company which are
purchasable hereunder, the Holder shall thereafter be entitled to purchase the
number of Warrant Shares or other securities resulting from such adjustment at
an Exercise Price per Warrant Share or other security obtained by multiplying
the Exercise Price in effect immediately prior to such adjustment by the number
of Warrant Shares purchasable pursuant hereto immediately prior to such
adjustment and dividing by the number of Warrant Shares or other securities of
the Company resulting from such adjustment. An adjustment made pursuant to this
paragraph shall become effective immediately after the effective date of such
event retroactive to the record date, if any, for such event.

            12. Reorganization, Reclassification, Merger, Consolidation or
Disposition of Assets. In case the Company shall reorganize its capital,
reclassify its capital stock, consolidate or merge with or into another
corporation (where the Company is not the surviving corporation or where there
is a change in or distribution with respect to the Common Stock of the Company),
or sell, transfer or otherwise dispose of all or substantially all its property,
assets or business to another corporation and, pursuant to the terms of such
reorganization, reclassification, merger, consolidation or disposition of
assets, shares of common stock of the successor or acquiring corporation, or any
cash, shares of stock or other securities or property of any nature whatsoever
(including warrants or other subscription or purchase rights) in addition to or
in lieu of common stock of the successor or acquiring corporation ("Other
Property"), are to be received by or distributed to the holders of Common Stock
of the Company, then the Holder shall have the right thereafter to receive upon
exercise of this Warrant, the number of shares of Common Stock of the successor
or acquiring corporation or of the Company, if it is the surviving corporation,
and Other Property receivable upon or as a result of such reorganization,
reclassification, merger, consolidation or disposition of assets by a Holder of
the number of shares of Common Stock for which this Warrant is exercisable
immediately prior to such event. In case of any such reorganization,
reclassification, merger, consolidation or disposition of assets, the successor
or acquiring corporation (if other than the Company) shall expressly assume the
due and punctual observance and performance of each and every covenant and
condition of this Warrant to be performed and observed by the Company and all
the obligations and liabilities hereunder, subject to such modifications as may
be deemed appropriate (as determined in good faith by resolution of the Board of
Directors of the Company) in order to provide for adjustments of Warrant Shares
for which this Warrant is exercisable which shall be as nearly equivalent as
practicable to the adjustments provided for in this Section 12. For purposes of
this Section 12, "common stock of the successor or acquiring corporation" shall
include stock of such corporation of any class which is not preferred as to
dividends or assets over any other class of stock of such corporation and which
is not subject to redemption and shall also include any evidences of
indebtedness, shares of stock or other securities which are convertible into or
exchangeable for any such stock, either immediately or upon the arrival of a
specified date or the happening of a specified event and any warrants or other
rights to subscribe for or purchase any such stock. The foregoing provisions of
this Section 12 shall similarly apply to successive reorganizations,
reclassifications, mergers, consolidations or disposition of assets.

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<PAGE>

            13. Call Provision. Beginning one year after the Registration
Statement has become effective, the Company shall have the right, upon five (5)
business days' prior written notice to the Holder (the "Call Right Notice"), to
call this Warrant, provided that (i) the Warrant Shares are registered for
resale pursuant to the Securities Act or are freely tradable without restriction
or legend, (ii) the Common Stock shall be listed or quoted for trading on the
Nasdaq Stock Market or a national securities exchange immediately preceding the
date of the Call Right Notice and (ii) the volume weighted average price (as
reported by Bloomberg LP) for 25 of the 30 business days immediately preceding
the date of the Call Right Notice were equal to or greater than $15.00 (subject
to adjustment for reverse and forward stock splits, stock dividends, stock
combinations and other similar transactions of the Common Stock that occur after
the date of this Warrant). If this Warrant has not been exercised in full upon
the expiration of such 5 business day notice period, this Warrant shall
terminate automatically without any further action on the part of the Holder or
the Company.

            14. Notice of Adjustment. Whenever the number of Warrant Shares or
number or kind of securities or other property purchasable upon the exercise of
this Warrant or the Exercise Price is adjusted, as herein provided, the Company
shall give notice thereof to the Holder, which notice shall state the number of
Warrant Shares (and other securities or property) purchasable upon the exercise
of this Warrant and the Exercise Price of such Warrant Shares (and other
securities or property) after such adjustment, setting forth a brief statement
of the facts requiring such adjustment and setting forth the computation by
which such adjustment was made. 15. Notice of Corporate Action. If at any time:

                  (a) the Company shall take a record of the holders of its
      Common Stock for the purpose of entitling them to receive a dividend or
      other distribution, or any right to subscribe for or purchase any
      evidences of its indebtedness, any shares of stock of any class or any
      other securities or property, or to receive any other right, or

                  (b) there shall be any capital reorganization of the Company,
      any reclassification or recapitalization of the capital stock of the
      Company or any consolidation or merger of the Company with, or any sale,
      transfer or other disposition of all or substantially all the property,
      assets or business of the Company to, another corporation or,

                  (c) there shall be a voluntary or involuntary dissolution,
      liquidation or winding up of the Company;

then, in any one or more of such cases, the Company shall give to Holder (i) at
least 20 days' prior written notice of the date on which a record date shall be
selected for such dividend, distribution or right or for determining rights to
vote in respect of any such reorganization, reclassification, merger,
consolidation, sale, transfer, disposition, liquidation or winding up, and (ii)
in the case of any such reorganization, reclassification, merger, consolidation,
sale, transfer, disposition, dissolution, liquidation or winding up, at least 20
days' prior written notice of the date when the same shall take place. Such
notice in accordance with the foregoing clause also shall specify (i) the date
on which any such record is to be taken for the purpose of such dividend,
distribution or right, the date on which the holders of Common Stock shall be
entitled

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<PAGE>

to any such dividend, distribution or right, and the amount and character
thereof, and (ii) the date on which any such reorganization, reclassification,
merger, consolidation, sale, transfer, disposition, dissolution, liquidation or
winding up is to take place and the time, if any such time is to be fixed, as of
which the holders of Common Stock shall be entitled to exchange their Warrant
Shares for securities or other property deliverable upon such disposition,
dissolution, liquidation or winding up. Each such written notice shall be
sufficiently given if addressed to Holder at the last address of Holder
appearing on the books of the Company and delivered in accordance with Section
17(d).

            16. Authorized Shares. The Company covenants that during the period
the Warrant is outstanding, it will reserve from its authorized and unissued
Common Stock a sufficient number of shares to provide for the issuance of the
Warrant Shares upon the exercise of any purchase rights under this Warrant. The
Company further covenants that its issuance of this Warrant shall constitute
full authority to its officers who are charged with the duty of executing stock
certificates to execute and issue the necessary certificates for the Warrant
Shares upon the exercise of the purchase rights under this Warrant. The Company
will take all such reasonable action as may be necessary to assure that such
Warrant Shares may be issued as provided herein without violation of any
applicable law or regulation, or of any requirements of the Trading Market upon
which the Common Stock may be listed.

                  Except and to the extent as waived or consented to by the
Holder, the Company shall not by any action, including, without limitation,
amending its certificate of incorporation or through any reorganization,
transfer of assets, consolidation, merger, dissolution, issue or sale of
securities or any other voluntary action, avoid or seek to avoid the observance
or performance of any of the terms of this Warrant, but will at all times in
good faith assist in the carrying out of all such terms and in the taking of all
such actions as may be necessary or appropriate to protect the rights of Holder
as set forth in this Warrant against impairment. Without limiting the generality
of the foregoing, the Company will (a) not increase the par value of any Warrant
Shares above the amount payable therefor upon such exercise immediately prior to
such increase in par value, (b) take all such action as may be necessary or
appropriate in order that the Company may validly and legally issue fully paid
and nonassessable Warrant Shares upon the exercise of this Warrant, and (c) use
commercially reasonable efforts to obtain all such authorizations, exemptions or
consents from any public regulatory body having jurisdiction thereof as may be
necessary to enable the Company to perform its obligations under this Warrant.

                  Before taking any action which would result in an adjustment
in the number of Warrant Shares for which this Warrant is exercisable or in the
Exercise Price, the Company shall obtain all such authorizations or exemptions
thereof, or consents thereto, as may be necessary from any public regulatory
body or bodies having jurisdiction thereof.

            17. Miscellaneous.

                  (a) Jurisdiction. This Warrant shall constitute a contract
      under the laws of New York, without regard to its conflict of law,
      principles or rules.

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<PAGE>

                  (b) Restrictions. The Holder acknowledges that the Warrant
      Shares acquired upon the exercise of this Warrant, if not registered, will
      have restrictions upon resale imposed by state and federal securities
      laws.

                  (c) Nonwaiver. No course of dealing or any delay or failure to
      exercise any right hereunder on the part of Holder shall operate as a
      waiver of such right or otherwise prejudice Holder's rights, powers or
      remedies, notwithstanding all rights hereunder terminate on the
      Termination Date.

                  (d) Notices. Any notice, request or other document required or
      permitted to be given or delivered to the Holder by the Company shall be
      delivered in accordance with the notice provisions of the Purchase
      Agreement.

                  (e) Successors and Assigns. Subject to applicable securities
      laws, this Warrant and the rights and obligations evidenced hereby shall
      inure to the benefit of and be binding upon the successors of the Company
      and the successors and permitted assigns of Holder. The provisions of this
      Warrant are intended to be for the benefit of all Holders from time to
      time of this Warrant and shall be enforceable by any such Holder or holder
      of Warrant Shares.

                  (f) Limitation of Liability. No provision hereof, in the
      absence of any affirmative action by Holder to exercise this Warrant or
      purchase Warrant Shares, and no enumeration herein of the rights or
      privileges of Holder, shall give rise to any liability of Holder for the
      purchase price of any Common Stock or as a stockholder of the Company,
      whether such liability is asserted by the Company or by creditors of the
      Company.

                  (g) Remedies. Holder, in addition to being entitled to
      exercise all rights granted by law, including recovery of damages, will be
      entitled to specific performance of its rights under this Warrant. The
      Company agrees that monetary damages would not be adequate compensation
      for any loss incurred by reason of a breach by it of the provisions of
      this Warrant and hereby agrees to waive the defense in any action for
      specific performance that a remedy at law would be adequate.

                  (h) Amendment. This Warrant may be modified or amended or the
      provisions hereof waived with the written consent of the Company and the
      Holder.

                  (i) Severability. Wherever possible, each provision of this
      Warrant shall be interpreted in such manner as to be effective and valid
      under applicable law, but if any provision of this Warrant shall be
      prohibited by or invalid under applicable law, such provision shall be
      ineffective to the extent of such prohibition or invalidity, without
      invalidating the remainder of such provisions or the remaining provisions
      of this Warrant.

                  (j) Headings. The headings used in this Warrant are for the
      convenience of reference only and shall not, for any purpose, be deemed a
      part of this Warrant.

                              ********************

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<PAGE>

            IN WITNESS WHEREOF, the Company has caused this Warrant to be
executed by its officer thereunto duly authorized.

Dated: ________, 2004

                                  AXONYX, INC.

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

                                       10
<PAGE>

                               NOTICE OF EXERCISE

To: Axonyx, Inc.

            (1) The undersigned hereby elects to purchase ________ Warrant
Shares of Axonyx, Inc. pursuant to the terms of the attached Warrant, and
tenders herewith such Warrant and payment of the exercise price in full,
together with all applicable transfer taxes, if any.

            (2) Payment shall take the form of (check applicable box):

                  |_| in lawful money of the United States; or

                  |_| the cancellation of such number of Warrant Shares as is
                  necessary, in accordance with the formula set forth in
                  subsection 3(d), to exercise this Warrant with respect to the
                  maximum number of Warrant Shares purchasable pursuant to the
                  cashless exercise procedure set forth in subsection 3(d).

            (3) Please issue a certificate or certificates representing said
Warrant Shares in the name of the undersigned or in such other name as is
specified below:

                  ________________________________________

The Warrant Shares shall be delivered to the following:

                  ________________________________________

                  ________________________________________

                  ________________________________________

            (3) Accredited Investor. The undersigned is an "accredited investor"
as defined in Regulation D promulgated under the Securities Act of 1933, as
amended.

                                        [PURCHASER]

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

                                        Dated:
                                               ----------------------------

<PAGE>

                                 ASSIGNMENT FORM

                    (To assign the foregoing warrant, execute
                   this form and supply required information.
                 Do not use this form to exercise the warrant.)

            FOR VALUE RECEIVED the foregoing Warrant and all rights evidenced
thereby are hereby assigned to

_______________________________________________ whose address is

_______________________________________________________________.

_______________________________________________________________

                                                Dated:  ______________, _______

                 Holder's Signature:    _____________________________

                 Holder's Address:      _____________________________

                                        _____________________________

Signature Guaranteed: ___________________________________________

NOTE: The signature to this Assignment Form must correspond with the name as it
appears on the face of the Warrant, without alteration or enlargement or any
change whatsoever, and must be guaranteed by a bank or trust company. Officers
of corporations and those acting in a fiduciary or other representative capacity
should file proper evidence of authority to assign the foregoing Warrant.Supplemental Indenture, dated  January 7, 2004, relating to 9 1/2% Senior Notes

 Exhibit 4.1 
  

CROWN CASTLE INTERNATIONAL CORP. 
  
 As Issuer 
  

  
  
 $114,265,000 aggregate principal amount 
  
 91⁄2% Senior Notes due 2011 
  

  
  
 SUPPLEMENTAL INDENTURE 
  
 Dated as of January 7, 2004 
  

  
 Supplementing the Indenture dated as of August 3, 1999, between Crown Castle International 
 Corp., as Issuer, and The Bank of New York, as successor trustee to United States Trust 
 Company of New York, as Trustee 

 

  
 THE BANK OF NEW YORK 
  
 As Trustee 
  

  
  

 SUPPLEMENTAL INDENTURE dated as of January 7, 2004, between Crown Castle International Corp., a Delaware
corporation (the “Company”), and The Bank of New York, as successor trustee to United States Trust Company of New York (the “Trustee”), as Trustee under the Indenture referred to herein. 
  
 WHEREAS the Company and the Trustee heretofore executed and delivered an
Indenture dated as of August 3, 1999 (the “Indenture”), in respect of the Company’s $114.265 million aggregate principal amount outstanding of 91⁄2% Senior Notes due 2011 (the “Securities”); 
  
 WHEREAS Section 9.02 of the Indenture provides that the Company and the
Trustee may amend the Indenture with the consent of the Holders of at least a majority in aggregate principal amount of the Securities then outstanding; 
  
 WHEREAS, pursuant to the Offer to Purchase and Consent Solicitation Statement dated December 5, 2003 (as amended, supplemented or modified, the
“Offer to Purchase”), the Company commenced a cash tender offer for any and all outstanding Securities and solicited the consents of the Holders of the Securities to amend certain provisions of the Indenture, as set forth in Article I
hereof; 
  
 WHEREAS the Holders of a majority in aggregate
principal amount of the Securities outstanding have consented to the amendments effected by this Supplemental Indenture; and 
  
 WHEREAS this Supplemental Indenture has been duly authorized by all necessary corporate action on the part of the Company. 
  
 NOW, THEREFORE, the Company and the Trustee agree as follows for the equal
and ratable benefit of the Holders of the Securities: 
  
 ARTICLE I 
  
 Amendments 

 
 SECTION 1.01. Amendments to Articles 4 and 5. Effective upon the
date hereof, each of Section 4.02 (Maintenance of Office or Agency), Section 4.03 (Reports), Section 4.04 (Compliance Certificate), Section 4.05 (Taxes), Section 4.06 (Stay, Extension and Usury Laws), Section 4.07 (Restricted Payments), Section 4.08
(Dividend and Other Payment Restrictions Affecting Subsidiaries), Section 4.09 (Incurrence of Indebtedness and Issuance of Preferred Stock), Section 4.10 (Asset Sales), Section 4.11 (Transactions with Affiliates), Section 4.12 (Liens), Section 4.13
(Business Activities), Section 4.14 (Corporate Existence), Section 4.15 (Offer to Repurchase Upon Change of Control), Section 4.16 (Sale and Leaseback Transactions), Section 4.17 (Limitation on Issuances and Sales of Capital Stock of Restricted
Subsidiaries), Section 4.18 (Limitation on Issuances of Guarantees of Indebtedness) and Section 5.01 (Merger, Consolidation, or Sale of Assets) of the Indenture is hereby deleted in its entirety and replaced with the 

 phrase “[Intentionally Omitted]”. All references to such deleted sections are also hereby deleted in their
entirety. 
  
 SECTION 1.02. Amendments to Article 6.
Effective upon the date hereof, each of clauses (3), (4), (5), (6), (7) and (8) of Section 6.01 is hereby deleted in its entirety and replaced with the phrase “[Intentionally Omitted]”. All references to such deleted clauses are also
hereby deleted in their entirety. 
  
 SECTION 1.03.
Trustee’s Acceptance. The Trustee hereby accepts this Supplemental Indenture and agrees to perform the same under the terms and conditions set forth in the Indenture. 
  
 ARTICLE II 
  
 Miscellaneous 
  
 SECTION 2.01. Interpretation. Upon execution and delivery of this Supplemental Indenture, the Indenture shall be modified and amended in accordance
with this Supplemental Indenture, and all the terms and conditions of both shall be read together as though they constitute one instrument, except that, in case of conflict, the provisions of this Supplemental Indenture will control. The Indenture,
as modified and amended by this Supplemental Indenture, is hereby ratified and confirmed in all respects and shall bind every Holder of Securities. In case of conflict between the terms and conditions contained in the Securities and those contained
in the Indenture, as modified and amended by this Supplemental Indenture, the provisions of the Indenture, as modified and amended by this Supplemental Indenture, shall control. 
  
 SECTION 2.02. Conflict with Trust Indenture Act. If any provision of this Supplemental Indenture limits, qualifies or
conflicts with any provision of the TIA that is required under the TIA to be part of and govern any provision of this Supplemental Indenture, the provision of the TIA shall control. If any provision of this Supplemental Indenture modifies or
excludes any provision of the TIA that may be so modified or excluded, the provision of the TIA shall be deemed to apply to the Indenture as so modified or to be excluded by this Supplemental Indenture, as the case may be. 
  
 SECTION 2.03. Severability. In case any provision in this Supplemental
Indenture shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby. 
  
 SECTION 2.04. Terms Defined in the Indenture. All capitalized terms not otherwise defined herein shall have the
meanings ascribed to them in the Indenture. 
  
 SECTION 2.05.
Headings. The Article and Section headings of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part of this Supplemental Indenture and shall in no way modify or restrict any of the
terms or provisions hereof. 

 SECTION 2.06. Benefits of Supplemental Indenture, etc. Nothing in this Supplemental Indenture or
the Securities, express or implied, shall give to any Person, other than the parties hereto and thereto and their successors hereunder and thereunder and the Holders of the Securities, any benefit of any legal or equitable right, remedy or claim
under the Indenture, this Supplemental Indenture or the Securities. 
  
 SECTION 2.07. Successors. All agreements of the Company in this Supplemental Indenture shall bind its successors. All agreements of the Trustee in this Supplemental Indenture shall bind its successors. 
  
 SECTION 2.08. Trustee Not Responsible for Recitals. The recitals
contained herein shall be taken as the statements of the Company and the Trustee assumes no responsibility for their correctness. 
  
 SECTION 2.09. Certain Duties and Responsibilities of the Trustee. In entering into this Supplemental Indenture, the Trustee shall be entitled to
the benefit of every provision of the Indenture relating to the conduct or affecting the liability or affording protection to the Trustee, whether or not elsewhere herein so provided. 
  
 SECTION 2.10. Governing Law. This Supplemental Indenture shall be governed by, and construed in accordance with, the
laws of the State of New York but without giving effect to applicable principles of conflicts of law to the extent that the application of the laws of another jurisdiction would be required thereby. 
  
 SECTION 2.11. Counterpart Originals. The parties may sign any number
of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. 
  

 IN WITNESS WHEREOF, each party hereto has caused this Supplemental Indenture to be signed by its officer
thereunto duly authorized as of the date first written above. 
  

	 CROWN CASTLE INTERNATIONAL CORP.,

		
	 by
	 	 /s/    W. Benjamin Moreland

	 	

	 Name:
 Title:
	 	 W. Benjamin Moreland
 Senior Vice President and
 Chief Financial Officer

  
  

	 THE BANK OF NEW YORK, as Trustee,

		
	by	 	 /s/    Margaret M. Ciesmelewski

	 	

	 Name:
 Title:
	 	 Margaret M. Ciesmelewski
 Vice President

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