EXHIBIT 4.5


                                  AMENDMENT TO

                    WARRANT TO PURCHASE 200,000 COMMOM SHARES

                                U.S. ENERGY CORP.


          WHEREAS,  SHAMROCK  PARTNERS,  LTD. of 111 Veterans Square,  Media, PA
     19063 ("Holder") was granted a warrant to purchase 200,000 common shares of
     U.S.  Energy  Corp.  $.01 par value  common  stock on  January 9, 1996 (the
     "Warrant"), with an Expiration Date of January 9, 1997.

          NOW THEREFORE, U.S. Energy Corp. hereby extends the Expiration Date of
     the Warrant to July 9, 1997.


        DATED, nunc pro tunc January 8, 1997.


                                                      U.S. ENERGY CORP.



                                                 By:     /s/ John L. Larsen
                                                      --------------------------
                                                      JOHN L. LARSEN, President