Agents which are curable by ultraviolet radiation are based on a binder formulation of (1) from 99.0 to 20% by weight of a copolymer, (2) from 1.0 to 80% by weight of monoolefinically unsaturated compounds and (3) from 0.0 to 20% by weight of polyolefinically unsaturated compounds. The agents contain copolymers (1) which are obtainable by subjecting a mixture of (A) from 80 to 99.9% by weight of olefinically unsaturated monomers, (B) from 0 to 10% by weight of a copolymerizable olefinically unsaturated photoinitiator and (C) from 0 to 10% by weight of a polymerization-regulating photoinitiator to free radical polymerization, the sum of (B) and (C) being not less than 0.1% by weight and the stated percentages by weight being based on the sum of the weights of (A)+(B)+(C).