Radiation-curable catalysts are obtainable by reactingA) 1 equivalent of a dihydric to hexahydric oxyalkylated C.sub.2 -C.sub.10 -alcohol withB) from 0.05 to 1 equivalent of a dibasic to tetrabasic C.sub.3 -C.sub.36 -carboxylic acid or its anhydride andC) from 0.1 to 1.5 equivalents of acrylic acid and/or methacrylic acidand reacting the excess carboxyl groups with an equivalent amount of epoxide compound, and are used in radiation-curable coating materials.