There are provided novel vulcanizable compositions based on optionally fully or partly hydrogenated nitrile rubbers containing epoxy groups, specific basic crosslinkers and crosslinking accelerators, as a result of which the use of conventional crosslinkers, such as sulphur in particular, is no longer required. The vulcanizates producible therefrom possess very good compression sets at room temperature, 100° C. and 150° C., and additionally exhibit high tensile stress combined with good elongation at break.