Vulcanizable composition comprising (i) at least one optionally fully or partly hydrogenated nitrile rubber containing epoxy groups and comprising repeat units derived from at least one conjugated diene, at least one α,β-unsaturated nitrile and optionally one or more further copolymerizable monomers, but not from a nonconjugated cyclic polyene, (ii) at least one Lewis and/or Brønsted acid as a crosslinker, where the Lewis acid is selected from the group of boron trifluoride, boron trihydride, aluminium trichloride, indium chloride, copper chloride, copper triflate, gold chloride, gold chloride, zinc chloride, zinc oxide, tin oxide, tin chloride, copper oxide, iron oxide, iron oxide, iron bromide, iron chloride, sulphur trioxide, silicon tetrachloride, lithium bromide, lithium chloride, magnesium oxide, magnesium chloride, scandium triflate, rhodium chloride and complexes of the following elements in the oxidation states of Co, Al, Fe, Fe, Ti, Sn, Co, Ni, Cu, Cu, Pb, Sn, Ag, Au, Au, Pd, Pt, Sc, Ir, Rh and In and the Brønsted acid is selected from the group consisting of sulphuric acid, hydrogensulphates, sulphurous acid, hydrogensulphites, hydrogen sulphide, hydrogensulphides, hydrogenphosphates, dihydrogenphosphates, diphosphonic acid, the partial esters thereof, metaphosphoric acid, triphosphonic acid, the partial esters thereof, hydrogencarbonates, acids of the halogens, hypohalous acids, halous acids, halic acids, perhalic acids, ammonium salts, inorganic and organic sulphonic acid, carboxylic acid, phosphonic acid, and the mono- or diesters thereof, and (iii) at least one crosslinking accelerator selected from the group consisting of thiurams, xanthogenates, thioureas, dithiocarbamates and carbamates, where crosslinkers other than those mentioned in (ii) are present in the vulcanizable composition only in an amount of less than 2.5 parts by weight based on 100 parts by weight of the optionally fully or partly hydrogenated nitrile rubber (i) containing epoxy groups, and crosslinking accelerators other than those mentioned in (iii) only in an amount of less than 2.5 parts by weight based on 100 parts by weight of the optionally fully or partly hydrogenated nitrile rubber (i) containing epoxy groups. (i) at least one optionally fully or partly hydrogenated nitrile rubber containing epoxy groups and comprising repeat units derived from at least one conjugated diene, at least one α,β-unsaturated nitrile and optionally one or more further copolymerizable monomers, but not from a nonconjugated cyclic polyene, (ii) at least one Lewis and/or Brønsted acid as a crosslinker, where the Lewis acid is selected from the group of boron trifluoride, boron trihydride, aluminium trichloride, indium chloride, copper chloride, copper triflate, gold chloride, gold chloride, zinc chloride, zinc oxide, tin oxide, tin chloride, copper oxide, iron oxide, iron oxide, iron bromide, iron chloride, sulphur trioxide, silicon tetrachloride, lithium bromide, lithium chloride, magnesium oxide, magnesium chloride, scandium triflate, rhodium chloride and complexes of the following elements in the oxidation states of Co, Al, Fe, Fe, Ti, Sn, Co, Ni, Cu, Cu, Pb, Sn, Ag, Au, Au, Pd, Pt, Sc, Ir, Rh and In and the Brønsted acid is selected from the group consisting of sulphuric acid, hydrogensulphates, sulphurous acid, hydrogensulphites, hydrogen sulphide, hydrogensulphides, hydrogenphosphates, dihydrogenphosphates, diphosphonic acid, the partial esters thereof, metaphosphoric acid, triphosphonic acid, the partial esters thereof, hydrogencarbonates, acids of the halogens, hypohalous acids, halous acids, halic acids, perhalic acids, ammonium salts, inorganic and organic sulphonic acid, carboxylic acid, phosphonic acid, and the mono- or diesters thereof, and (iii) at least one crosslinking accelerator selected from the group consisting of thiurams, xanthogenates, thioureas, dithiocarbamates and carbamates,