The invention relates to peroxide- or radiation-curable copolymer containing compositions and to the resulting radiation- or peroxide- cured compositions. The compositions may optionally contain a reinforcing filler. Copolymers employed in the compositions are acrylate modified copolymers of an isoolefin of 4 to 7 carbon atoms and para-alkylstyrene comonomers. Since the percentage of extractables from the cured composition is negligible, the cured compositions are suitable for use in the manufacture of a variety of high purity rubber goods used in the pharmaceutical and health care industries. In addition, the compositions may be employed as condenser packings and as food contact materials or wire cable insulation materials. Further, the cured composition may be employed in the manufacture of high purity hoses.