TECHNOLOGY FOCUS - POLYMERS - Preferred Component: The polymer used is a high-temperature-stable polymer containing nitrogen, oxygen, and/or sulfur atom in one repeating unit or in different repeating units. Polyazole(s) and/or polysulfones are used in the first step. The mixture prepared in the first step contains compounds of formula (=)y-R-(SO3Z)x, x(ZO3S)-R-C(=)-R-(SO3Z)x, or A-C(=)-R-(SO3Z)x.R = a bond, 1-15C alkyl group, 1-15C alkoxy group, ethylenoxy group, or 5-20C aryl or heteroaryl group, with the radications optionally substituted by halo, -OH, COOZ, -CN, or NZ2 (1); or bond, a divalent 1-15C alkylene group, divalent 1-15C alkylenoxy group, or a divalent 5-20C aryl or heteroaryl group, with the radicals optionally substituted by halo, -OH, COOZ, -CN, NZ2 (2);Z = H, 1-15C alkoxy group, ethylenoxy group, or 5-20C aryl or heteroaryl group, with the radicals optionally substituted by halo, -OH, or -CN;A = COOR2, CN, CONR22, OR2, or R2;R2 = (1); andx, y = 1-10.The mixture prepared in the first step comprises vinyl-containing phosphonic acid. It contains compounds of formula (=)y-R-(PO3Z2)x, x(Z2O3P)-R-C(=)-R-(PO3Z2)x, or A-C(=)-R-(PO3Z2)x. It contains monomers capable of crosslinking. The polymerization step is effected by a substance, which is capable of forming free radicals. It is carried out by irradiation with infrared light, near infrared light, UV light, beta-rays, gamma-rays, or electron beams. The membrane has a layer comprising a catalytically active component.Preferred Parameter: The weight ratio of vinyl-containing phosphonic acid to vinyl-containing sulfonic acid, is 1:100-99:1.Preferred Composition: The membrane comprises polymer (1-90 wt.%), and polyvinylsulfonic acid (99-0.5 wt.%). EXAMPLE - Polybenzimidazole (PBI) polymer (100 g) was treated in 89 % strength phosphoric acid (250 ml) at 160 degrees C for 4 hours. The excess acid was subsequently removed, and the solid was washed 3 times with water. The polymer obtained was subsequently neutralized twice with 10 % strength ammonium hydroxide (100 ml), and subsequently treated twice with distilled water. The polymer was subsequently treated at 160 degrees C for 1 hour. Vinylphosphonic acid (97 %) (500 g) was added to PBI polymer, and with gentle stirring, a homogeneous solution was formed after 4 hours at 150 degrees C. The homogeneous solution (150 g) was stirred slowly at 125 degrees C. Aqueous vinylsulfonic acid solution (4.6 g) was slowly added dropwise to the solution, producing a membrane by applying the solution to a polyethylene terephthalate support. The membrane was subsequently treated by an electron beam at a radiation dose of 33 kGy. It exhibited a conductivity of 8.0 and 13.2 mS/cm at 80 and 160 degrees C, respectively.