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                                                                   EXHIBIT 10.33


                             URANIUM RESOURCES, INC.

                          6.5% SECURED CONVERTIBLE NOTE

$1,500,000.00                                          June 30, 1999
                                                       Note No.

         FOR VALUE RECEIVED, the undersigned URANIUM RESOURCES, INC., a Delaware
corporation (the "Obligor" or "Uranium Resources"), hereby promises to pay to
LINDNER MARKET NEUTRAL FUND, a series of LINDNER INVESTMENTS, a Massachusetts
business trust, or its registered assigns (the "Purchaser") on December 31, 2000
the principal sum of ONE MILLION FIVE HUNDRED THOUSAND AND 00/100 DOLLARS
($1,500,000.00), and to pay interest on the unpaid principal balance hereof from
the date hereof at a rate of 6.5% per annum. Payment of interest shall be
deferred until the maturity date. This Note and any interest thereon may not be
transferred except as provided in the Note and Warrant Purchase Agreement dated
May 25, 1995, between Obligor and Purchaser, as supplemented by the Note and
Warrant Exchange Agreement, dated March 23, 1998, and as further supplemented
and amended by the Note Exchange Agreement dated June 30, 1999 (the "Note and
Warrant Purchase Agreement").

         This Note is issued pursuant to the Note and Warrant Purchase Agreement
and this Note and the holder hereof is entitled, equally and ratably with the
holders of all other Notes outstanding under the Note and Warrant Purchase
Agreement, to all of the benefits provided for thereby, including, but not
limited to the security granted to the Purchaser therein, and the benefits under
the Guaranty executed by the Mortgaging Subsidiary in connection therewith, and
shall be bound by all of the provisions set forth therein, to which Note
Purchase and Warrant Agreement reference is hereby made for a statement thereof.

         This Note is supported by the Guaranty of the Mortgaging Subsidiary,
which Guaranty will be secured by a lien and security interest in and upon the
Mortgaging Subsidiary's interest in the Collateral and the Texas Real Property.

         Subject to and upon compliance with the provisions of the Note and
Warrant Purchase Agreement, the Holder of this Note is entitled, at its option,
at any time, to convert this Note into fully paid and non-assessable shares of
Common Stock of the Obligor at the initial Conversion Price of $3.00 per share,
subject to such adjustment or adjustments, if any, of such Conversion Price and
the Common Stock issuable upon conversion, as may be required by the Note and
Warrant Purchase Agreement, upon surrender of this Note, duly endorsed or
assigned to the Obligor or in blank, to the Obligor, with the conversion notice
attached hereto, or accompanied by a separate written notice substantially in
the form of such conversion notice, duly executed by the Holder and stating that
the Holder hereof elects to convert this Note, or if less than the entire
principal amount hereof is to be converted, the portion hereof to be converted,
all in accordance with the provisions of the Note and Warrant Purchase
Agreement.


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         This Note is subject to mandatory conversion into shares of Common
Stock upon the occurrence of a Mandatory Conversion Event, as set forth in the
Note and Warrant Purchase Agreement. Accrued but unpaid interest is subject, at
the option of the Holder, to conversion into shares of Common Stock or, at the
option of the Holder, such interest shall be paid over a period of 18 months
after the earlier to occur of the maturity date or the Mandatory Conversion
Event, as set forth in the Note and Warrant Purchase Agreement.

         Except as otherwise provided in the Note and Warrant Purchase
Agreement, no payment or adjustment is to be made on conversion for interest
accrued hereon or for dividends issued on securities issued on conversion.

         No fractional shares will be issued on conversion, but instead of any
fractional interest, the Obligor shall pay a cash adjustment as provided in the
Note and Warrant Purchase Agreement.

         In the event any action is taken to collect or enforce the indebtedness
evidenced by this Note (the "Indebtedness") or any part thereof, the Obligor and
each endorser hereof agrees to pay, in addition to the principal and interest
due and payable hereon, all costs of collecting this Note, including reasonable
attorneys' fees and expenses. These costs shall include any expenses incurred by
the Purchaser in any bankruptcy, reorganization or other insolvency proceeding.

         Acceptance by the Purchaser of any payment in an amount less than the
amount then due and owing shall be deemed an acceptance on account only, and the
failure to pay the entire amount then due and owing shall cause the Purchaser
and endorsers to remain in default.

         The liability of the Obligor and any endorsers hereof, shall be joint
and several, absolute and unconditional, without regard to the liability of any
other party hereunder or under any other document or instrument executed in
connection with this Note.

         No delay or omission of any holder in exercising any right or rights
shall operate as a waiver of such right or any other rights. Waiver on one
occasion shall not be construed as a bar to or waiver of any right or remedy on
any future occasion.

         The liability of the Obligor under this Note (and the liability of any
endorsers and/or Guarantors of this Note) shall not be discharged, diminished or
in any way impaired by: (a) the release, impairment, discharge, substitution,
exchange, modification of or failure to obtain foreclose or realize on any
guaranty or any security granted Purchaser by any party for the Indebtedness;
(b) any waiver by Purchaser or failure to enforce or exercise rights under any
of the terms, covenants or conditions of this Note or any guaranty; (c) the
granting of any renewal, indulgence, extension of time to Obligor, or any other
obligors of the Indebtedness. or (d) the addition or release of any person or
entity primarily or secondarily liable for the Indebtedness.

         In no event shall the interest rate charged or received hereunder at
any time exceed the maximum interest rate permitted under applicable law.
Payments of interest received by Purchaser hereunder which would otherwise cause
the interest rate hereunder to exceed such


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maximum interest rate shall, to the extent of such excess, be deemed to be (and
deemed to have been contracted as being) prepayments of principal and applied as
such.

         Under certain circumstances, as specified in the Note and Warrant
Purchase Agreement, the principal of this Note may be declared due and payable
in the manner and with the effect provided in the Note and Warrant Purchase
Agreement.

         Transfer of this Note is subject to the Company's right of first offer
as set forth in the Note and Warrant Purchase Agreement.

         This Note shall be binding upon the undersigned and its successors and
assigns and shall inure to the benefit of Purchaser, its successors and assigns.
Every person and entity at any time liable for the payment of this Note hereby
waives demand, presentment, protest, notice of protest, note of nonpayment due
and all other requirements otherwise necessary to hold them immediately liable
for payment hereunder.

         This Note and the Note and Warrant Purchase Agreement are governed by
and shall be construed and enforced in accordance with Missouri law.

                                        URANIUM RESOURCES, INC.

                                        By: ___________________________________
                                              President

THIS NOTE HAS BEEN ACQUIRED FOR INVESTMENT AND HAS NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED (THE "1933 ACT"). THIS NOTE MAY NOT BE
PLEDGED OR OTHERWISE TRANSFERRED IN THE ABSENCE OF REGISTRATION UNDER THE 1933
ACT PROVIDED, HOWEVER, THAT THIS NOTE MAY BE PLEDGED OR OTHERWISE TRANSFERRED
PURSUANT TO AN EXEMPTION FROM REGISTRATION, INCLUDING, BUT NOT LIMITED TO, THOSE
PROVIDED IN RULE 144,144A OR 145 OR REGULATION S UNDER THE 1933 ACT. TRANSFER OF
THIS NOTE IS ALSO SUBJECT TO THE RESTRICTIONS, TERMS AND CONDITIONS SET FORTH IN
THAT CERTAIN NOTE AND WARRANT PURCHASE AGREEMENT DATED MAY 25, 1995, AS AMENDED,
AMONG URANIUM RESOURCES, INC., LINDNER INVESTMENTS, A COPY OF WHICH IS AVAILABLE
FOR INSPECTION AT THE OFFICE OF URANIUM RESOURCES, INC., AND WILL BE MADE
AVAILABLE BY URANIUM RESOURCES, INC. UPON WRITTEN REQUEST.



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                                   ASSIGNMENT

I/we assign and transfer $        principal amount of this Note No. R-     to

- ------------------------------------------------------------------------------
             (Print or type name, address and zip code of assignee)

Insert social security or other identifying number of assignee: ______________
and irrevocably appoint       as my/our agent and attorney-in fact to transfer
this Note or the portion hereof which has been so assigned, on the books of the
Company. The agent may substitute another to act for him or her.

Dated:                           Signed:
      -----------------------
                                 ----------------------------------------
Signature Guaranteed By:         [Name of  Noteholder--Sign exactly as name
                                 appears on the first page of this Note]

- -----------------------------    By:

                                 ----------------------------------------
                                      Its:



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                              NOTICE OF CONVERSION

TO Uranium Resources, Inc.:

The undersigned owner of this Secured Convertible Note hereby irrevocably
exercises the option to convert $ _______________principal amount of this
Secured Convertible Note, into shares of Common Stock of Uranium Resources,
Inc., in accordance with its terms, and directs that the shares of Common Stock
issuable and deliverable upon conversion be issued and delivered to the
undersigned unless a different note has been indicated below. If shares of
Common Stock are to be registered in the name of a person other than the
undersigned, the undersigned will pay any transfer taxes payable with respect
thereto.

Dated:
                               Signed:
                                      ------------------------------------------
                               Name of Noteholder
                               By:
                                  ----------------------------------------------
                               Its:

Fill in for registration of shares of Common Stock only if otherwise than in
name and address of the above named Noteholder:


- ---------------------------                -------------------------------
(Name)                                     (Address)


- -------------------------------            -------------------------------
(City and State)                           (Tax Identification Number)


(Please print name and address including zip code number)