Coating compounds curable by means of high-energy radiation, comprising as binder A) at least one (meth)acrylic copolymer containing olefinic double bonds capable of free-radical polymerization and hydroxyl groups with a C.dbd.C equivalent weight from 100 to 10,000 and an OH-value from 20 to 250 mg KOH/g, which is prepared from monomers comprising: A1) at least one olefinically unsaturated, epoxy-functional monomer capable of free-radical polymerization, A2) at least one olefinically unsaturated, carboxy-functional monomer capable of free-radical polymerization and A3) at least one further olefinically unsaturated monomer capable of free-radical polymerization which is different from A1) and A2), and B) at least one component with free isocyanate groups and process for multilayer coating using the coating compounds.