A process comprising applying coating materials to substrates, and curing the coating materials thermally and with actinic radiation, alone or together with optional coating films already present on the substrate. The actinic radiation cure is conducted under an oxygen-depleted atmosphere. The coating materials comprise (meth)acrylate copolymers having an OH number from 100 to 220 mg KOH/g, Tg of −35 to +60° C., number-average MW of from 1,000 to 10,000 daltons and a mass-average MW of from 2,000 to 40,000 daltons and contain in copolymerized form an amount of hydroxyl-containing monomers (a) that corresponds to the OH number, of which (a1) from 20 to 90% by weight are based on (a), 4-hydroxybutyl(meth)acrylate and/or 2-alkylpropane-1,3-diol mono(meth)acrylate, and (a2) from 10 to 80% by weight are based on (a), other hydroxyl-containing olefinically unsaturated monomers. The process further comprises from 0.2 to 8% by weight of photoinitiators.