1

Common Stock represented hereby on the date on which this Warrant was
surrendered and payment of the Purchase Price was made, irrespective of the date
of issue or delivery of such certificate.

         2. Transfer. (a) The Company will maintain books for the registration
and transfer of the Warrants, and any such transfer will be registrable thereon
upon surrender of the transferred Warrant to the Company's principal office,
together with a duly executed assignment thereof and funds sufficient to pay any
required stock transfer taxes. Upon such surrender and payment, the Company
shall, subject to Section 9, execute and deliver a new Warrant or Warrants in
the name of the assignees and in the number of shares of Common Stock specified
in the assignment and this Warrant shall promptly be canceled.

         (b) The Company covenants and agrees that (i) it will pay, when due and
payable, any and all stock transfer and similar taxes that may be payable in
respect of the issuance of this Warrant or of any shares of Common Stock
issuable upon exercise; and (ii) the Common Stock shall be deemed to be issued
to the Holder or its designee as the record owner of such shares as of the close
of business on the date on which this Warrant shall have been surrendered and
payment of the Exercise Price has been properly tendered for the purchase of
such shares.

         3. Certain Covenants of the Company. The Company covenants and agrees
that all shares of Common Stock that may be issued upon the exercise of the
rights represented by this Warrant will, upon issuance, be fully paid and
non-assessable and free from all taxes, liens, charges and security interests
with respect to the issue thereof. The Company further covenants and agrees that
during the period within which the rights represented by the Warrant may be
exercised, the Company will at all times have authorized, and reserved free of
preemptive or other rights for the exclusive purpose of issue upon exercise of
the rights evidenced by this Warrant, a sufficient number of shares of its
Common Stock to provide for the exercise of the rights represented by this
Warrant. The Company shall take all such actions as may be necessary to assure
that all such shares of Common Stock may be issued upon the exercise of the
rights represented by this Warrant without violation of any applicable law or
governmental regulation or any requirements of any domestic securities exchange
upon which shares of Common Stock may be listed (except for official notice of
issuance which shall be immediately delivered by the Company upon each such
issuance).

         4. Adjustment of Purchase Price and Number of Shares. The number of
shares of Common Stock with respect to which this Warrant is exercisable (the
"Exercise Rate") shall be subject to adjustment from time to time as follows:

                  a. In case the Company shall (x) pay a dividend in or make a
distribution of Common Stock on outstanding Common Stock, (y) subdivide
outstanding Common Stock into a larger number of shares of Common Stock by
reclassification or otherwise, or (z) combine outstanding Common Stock into a
smaller number of shares of Common Stock by reclassification or otherwise, the
Exercise Rate in effect immediately prior thereto shall be adjusted
proportionately so that the holder of this Warrant thereafter exercised shall be
entitled to receive the number of shares of the Common Stock that such holder
would have owned after the happening of any of the events described above had
such warrant been exercised immediately prior to the happening of such event. An
adjustment made pursuant to this subsection (a) shall become effective
retroactively to immediately after the record date in the case of a share
dividend or distribution and shall become effective immediately after the
effective date in the case of a subdivision or combination.

                  b. In case of any capital reorganization or reclassification
of the shares of Common Stock (except as provided in subsection (a) above), or
in case of any consolidation or merger to which the Company is a party (other
than a merger in which the Company is the surviving corporation and which does
not result in any capital reorganization or reclassification of Common Stock),
or in case of any sale or conveyance to another corporation of all or
substantially all of the property and assets of the Company, and if, in
connection with any such consolidation, merger, sale or conveyance, shares or
other securities or property shall be issuable or deliverable in exchange for
shares of Common Stock, provision shall be made 



                                       27

   2

as part of the terms of such capital reorganization or reclassification,
consolidation, merger, sale or conveyance that the holder of this Warrant
thereafter exercised shall have the right upon such exercise to receive the same
kind and amount of stock and other securities and property as would have been
receivable upon such capital reorganization or reclassification, consolidation,
merger, sale or conveyance by a holder of the number shares of Common Stock with
respect to which such Warrant might have been exercised immediately prior
thereto. In any such case, appropriate provision (as determined to be equitable
in the business judgment of the Board of Directors) shall be made for the
application of Section 4 with respect to the rights and interests thereafter of
the holder of this Warrant to the end that such Section (including adjustments
of the Exercised Rate) shall be reflected thereafter, as nearly as reasonably
practicable, in all subsequent exercises of this Warrant. The Company shall not
effect any such consolidation, merger or sale, unless prior to the consummation
thereof, the successor corporation (if other than the Company) resulting from
consolidation or merger or the corporation purchasing such assets assumes by
written instrument (in a manner determined to be equitable in the business
judgment of the Board of Directors to the holder of this Warrant), the
obligation to deliver to such holder such shares of stock, securities or assets
as, in accordance with the foregoing provisions, such holder may be entitled to
acquire.

                  c. In case the Company shall offer shares of Common Stock or
securities convertible into or exchangeable for Common Stock or rights, options
or warrants to subscribe for or purchase shares of its Common Stock or
securities convertible into or exchangeable for Common Stock (including, without
limitation, any offering of rights or warrants entitling holders of shares of
Common Stock to purchase Common Stock or securities convertible or exchangeable
into Common Stock) at a price per share equal to or less than $1.50 each, the
number of shares of its Common Stock with respect to which this Warrant is
exercisable thereafter shall be determined by multiplying the number of shares
of Common Stock with respect to which this Warrant was exercisable theretofore
by a fraction (not to be less than one), of which the numerator shall be the
number of shares of Common Stock outstanding immediately prior to such record
date plus the number of additional shares of Common Stock offered for
subscription or purchase, and of which the denominator shall be the number of
shares of Common Stock outstanding immediately prior to such record date plus
the number of shares of Common Stock which the aggregate offering price of the
total number of shares being offered would purchase at $1.50 per share. Such
adjustment shall be made whenever such Common Stock or rights, options or other
securities are issued and shall become retroactively effective immediately after
the record date. This paragraph c. shall not apply to the Warrants that were
issued in connection with the Series E Redeemable Convertible Preferred Stock
which was issued on or about October 31, 1996

         The foregoing provisions for adjustment of the Exercise Rate shall
apply in each successive instance in which an adjustment is required thereby. No
adjustment in the Exercise Rate resulting from the application of the foregoing
provisions is to be given effect unless, by making such adjustment, the Exercise
Rate in effect immediately prior to such adjustment would be changed thereby by
1% or more, but any adjustment that would change the Exercise Rate by less than
1% is to be carried forward and given effect in making future adjustments. All
calculations under this Section 4 shall be made to the nearest one-hundredth
(1/100th) of a share. Shares of Common Stock owned by or held for the account of
the Company shall not be deemed to be outstanding for the purposes of any
computation made under this Section 4.

         Whenever the number of shares of Common Stock deliverable upon the
exercise of this Warrant shall be adjusted pursuant to the provisions hereof,
the Company shall forthwith file at its principal office and with any transfer
agent for the Common Stock a statement, signed by the President or one of the
Vice-Presidents of the Company and by its Treasurer or one of its Assistant
Treasurers, stating the adjusted number of shares of Common Stock deliverable
with respect to this Warrant and setting forth in reasonable detail the method
of calculation and the facts requiring such adjustment and upon which such
calculation is based, and shall mail a notice of such adjustment to the holder
of record of this Warrant. Each adjustment shall remain in effect until a
subsequent adjustment hereunder is required.



                                       28

   3

In the event:

         (x) of the occurrence of any of the events referred to in subsections
         (a), (b) and (c) above; or

         (y) of any liquidation, dissolution or winding up of the Company (a
         "Liquidation");

then the Company shall cause to be mailed to the holder of record of this
Warrant at least 20 days prior to the applicable date hereinafter specified, a
notice describing the event and stating the effect, if any, that such event will
have upon the Exercise Rate, and (A) the date on which a record is to be taken
for the purpose of a distribution referred to in subsections (a) or (c) above,
or, if a record is not to be taken, the date as of which the holders of Common
Stock of record to be entitled to such distribution are to be determined, or (B)
the date on which any subdivision, combination or other capital reorganization
or reclassification or any consolidation, merger, sale or conveyance referred to
in subsections (a) or (b) above or such Liquidation is expected to become
effective.

         In the case of rights, options, warrants or convertible or exchangeable
securities being issued, the price per share of Common Stock shall be determined
by dividing (x) the total amount receivable by the Company in consideration of
the sale and issuance of such rights, options, warrants or convertible or
exchangeable securities, plus the total consideration payable to the Company
upon exercise, conversion or exchange thereof, by (y) the total number of shares
of such class or series of Common Stock covered by such rights, options,
warrants or convertible or exchangeable securities. In case the Company shall
sell and issue shares of any class or series of Common Stock, or options,
warrants or convertible or exchangeable securities containing the right to
subscribe for or purchase shares of any class or series of Common Stock, for a
consideration consisting, in whole or in part, of property other than cash or
its equivalent, then in determining the consideration received by the Company
for purposes hereof, the Board of Directors of Company shall determine, in good
faith, the fair value of the property.

         The Company will at all times during the Exercise Period reserve and
keep available for issuance upon exercise of this Warrant the number of shares
of Common Stock that is equal to the Exercise Rate; provided, however, that
nothing contained herein shall be construed to preclude the Company from
satisfying its obligations in respect of the exercise of this Warrant by
delivery of shares of Common Stock that are held in the treasury of the Company.
The Company covenants that all shares of Common Stock that shall be issued upon
exercise of this Warrant will, upon issue, be fully paid and nonassessable and
not subject to any preemptive rights.

         The shares of Common Stock issuable upon exercise of this Warrant when
the same shall be issued in accordance with the terms hereof are hereby declared
to be and shall be fully paid nonassessable shares of Common Stock and not
liable to any calls or assessments thereon, and the holders thereof shall not be
liable for any further payments in respect thereof.

         "Common Stock" when used in Section 4 with reference to the Common
Stock with respect to which this Warrant is exercisable, shall mean only Common
Stock as authorized by the Restated Certificate of Incorporation of the Company,
as amended to the date hereof, and any shares into which such Common Stock may
thereafter have been changed, and, when otherwise used in Section 4, shall also
include shares of the Company of any other class or series, whether now or
hereafter authorized, that ranks or is entitled to participation, as to payment
of assets upon Liquidation and payment of dividends, substantially on a parity
with such Common Stock or other class of shares into which such Common Stock may
have been changed.

         The Company will not, by amendment of 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 to be observed
or performed hereunder by the company, but will at all times in good faith
assist in the carrying out of all the provisions of this Section 4 and in the
taking of all such action as may be necessary or appropriate in order to protect
the conversion privilege of the holders of this Warrant against dilution or
other impairment. Without limiting the generality of the foregoing, the Company
(1) will not increase the par 



                                       29

   4

value of any shares of stock receivable upon exercise of this Warrant above the
Purchase Price then in effect, and (2) will take all such actions as may be
necessary or appropriate in order that the Company may validly and legally issue
fully paid and nonassessable shares of stock upon the exercise in full of this
Warrant from time to time outstanding.

         5. Fractional Interests. The Company shall not be required to issue
fractional shares on the exercise of a Warrant. If any faction of a share would
be issuable on the exercise of a Warrant (or specified portion thereof), the
Company shall pay an amount in cash equal to the Current Market Price per share
of Common Stock (as defined in Section 6) multiplied by such fraction.

         6. Definition of Current Market Value. (a) The "Current Market Price"
on any given day shall be: (i) if the Common Stock is listed or admitted to
unlisted trading privileges on any exchange registered with the Securities and
Exchange Commission as a national securities exchange" under the Securities
Exchange Act of 1934 (a "National Securities Exchange"), the last sales price of
the shares of Common Stock on the National Securities Exchange in or nearest the
City of New York on which the shares of Common Stock shall be listed or admitted
to unlisted trading privileges (or the quoted closing bid if there be no sales
on such National Securities Exchange) on the most recently completed trading day
prior to such day; or (ii) if the Common Stock is not so listed or admitted, the
closing sales price of a share of Common Stock as quoted in The Nasdaq Stock
Market on the most recently completed trading day prior to the day in question;
or (iii) if the Common Stock is not so quoted, the mean between the high and low
bid prices of the shares of Common Stock in the over-the-counter market on the
most recently completed trading day prior to the day in question as reported by
National Quotation Bureau Incorporated or similar organization. If the Company's
Common Stock is not traded or a price is not quoted as set forth above, Current
Market Price shall be Fair Market Value.

                  (b) "Fair Market Value" shall be determined (i) in good faith
         by the Board of Directors of the Company, or (ii) if the holder of this
         Warrant disagrees with the Fair Market Value as so determined pursuant
         to subsection (i), it must notify the Company in writing of such
         disagreement within twenty days after receiving notice of the Board of
         Directors' determination and include in such notice the holder's
         estimate of the Fair Market Value, in which event the Fair Market Value
         shall then be determined by an investment banking firm chosen by the
         Company which is satisfactory to and approved by the holder (the
         "Independent Financial Expert").

         If the Company and the holder are unable to agree upon an investment
banking firm to act as the Independent Financial Expert within ten days after
the notice from Holder provided for in subsection (b)(ii) above, then each party
will within ten days thereafter select an investment banking firm and the two
investment banking firms so selected shall select a third investment banking
firm within ten days and such third investment banking firm shall, as the
Independent Financial Expert, determine the Fair Market Value. If either party
fails to timely designate its investment banking firm as provided above then the
investment banking firm selected by the other party shall act as Independent
Financial Expert to determine Fair Market Value. The Independent Financial
Expert shall use one or more valuation methods that it, in its professional
judgment, determines to be most appropriate. The decision of the Independent
Financial Expert so selected shall be final and binding upon all parties. The
Company shall bear the costs of the chosen investment banking firms.

         7. Taking of Record; Stock and Warrant Transfer Books. In the case of
all dividends or other distributions by the Company to the holders of its Common
Stock with respect to which any provision of Section 4 refers to the taking of a
record of such holders, the Company will in each such case take such a record
and will take such record as of the close of business on a Business Day. The
Company will not at any time, except upon dissolution, liquidation or winding up
of the Company, close its stock transfer books or Warrant transfer books so as
to result in preventing or delaying the exercise or transfer of any Warrant.

         8. Restrictions on Transferability. This Warrant was originally issued
in a transaction exempt from the registration requirements of the Securities Act
of 1933, as amended (the "Securities Act"), and 


                                       30

   5

neither this Warrant nor any shares of Common Stock issuable upon the exercise
hereof were then registered under the Securities Act. Unless this Warrant or
such shares were subsequently registered under the Securities Act and sold by
the holder thereof in accordance with such registration, this Warrant or such
shares, as the case may be, may not be sold by the holder hereof or of such
shares unless this Warrant or such shares is or are subsequently registered
under the Securities Act or an exemption from such registration is available.
The shares of Common Stock issuable hereunder will bear an appropriate
restrictive legend as is required by the Securities Act or any state blue sky
laws. The holder of this Warrant, by acceptance of this Warrant, agrees to be
bound by the provisions of this Section and represents to the Company that it is
acquiring the Warrant and the Common Stock issuable hereunder solely for its own
account, for the purpose of investment and not with a view to distributing or
selling it or any part thereof in violation of the Securities Act, but subject,
nevertheless, to any requirement of law that the disposition of such holder's
property be at all times within its control.

         9. Replacement. Upon receipt of evidence reasonably satisfactory to the
Company (an affidavit of the registered holder shall be satisfactory) of the
ownership and the loss, theft, destruction or mutilation of this Warrant, and in
the case of any such loss, theft or destruction, upon receipt of indemnity
reasonably satisfactory to the Company (provided that the holder's own agreement
shall be satisfactory), or, in the case of any such mutilation upon surrender of
this Warrant, the Company shall (at its expense) execute and deliver in lieu of
this Warrant a new warrant of like kind dated the date of such lost, stolen,
destroyed or mutilated Warrant.

         10. Notice Generally. Any notice, demand or delivery pursuant to the
provisions hereof shall be sufficiently given or made if sent by first class
mail, postage prepaid, addressed to the holder of this Warrant or of the Common
Stock issued upon the exercise hereof at the holder's last known address
appearing on the books of the Company, or, except as herein otherwise expressly
provided, to the Company at its main office, Attention of the President, or such
other address as shall have been furnished to the party giving or making such
notice, demand or delivery.

         11. Voting Rights, Dividends. This Warrant does not grant the holder
hereof any voting rights or other rights as a stockholder of the Company. No
dividends are payable or will accrue on this Warrant or the shares purchasable
hereunder until, and except to the extent that, this Warrant is exercised.

         12.  GOVERNING LAW.  THIS WARRANT SHALL BE GOVERNED BY THE
LAW OF THE STATE OF DELAWARE.

         IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed this 13th day of November, 1998.


                                         AMERICAN ECOLOGY CORPORATION



                                         By: /s/ Jack K. Lemley
                                            -----------------------------------
                                         Name:   Jack K. Lemley
                                         Title:  Chief Executive Officer




                                       31

   6




                               SUBSCRIPTION NOTICE


                 (To be executed only upon exercise of Warrant)


         _______________________________________, being the undersigned
registered owner of this Warrant irrevocably exercises this Warrant for and
purchases ______ shares of the Common Stock, par value $.01 per share (the
"Common Stock"), of American Ecology Corporation, constituting all or part of
the shares of Common Stock purchasable with this Warrant, and herewith makes
payment therefor, all at the price and on the terms and conditions specified in
this Warrant and requests that certificates for the shares of Common Stock
hereby purchased (and any securities or other property issuable upon such
exercise) together with, if such certificates do not represent all the shares of
Common Stock purchasable with this Warrant, a new Warrant, identical to the
canceled Warrant except with respect to the number of shares of Common Stock
evidenced thereby, for the remaining unsold shares of Common Stock, be issued in
the name of and delivered to the undersigned at the address set forth below.



Dated:
      -----------------------------      --------------------------------------
                                          Name of Warrant Holder


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



                                          -------------------------------------
                                          Street Address



                                          -----------------------------------
                                          City            State      Zip Code










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