By means of a curing process combining thermal and UV curing it is possible, using compositions comprising (A) a coating system based on a polyacrylate polyol or polyester polyol with melamine, or a polyacrylate polyol and/or polyester polyol with a blocked or unblocked polyisocyanate, or a carboxyl-, anhydride- or amino-functional polyester and/or polyacrylate with an epoxy-functional polyester or polyacrylate, (B) an OHnull, NH2null, COOHnull, epoxy- or NCO-functional resin containing, in addition, at least one ethylenically unsaturated double bond, which is separated from the functional group by a spacer group, and (C) at least one photoinitiator, to obtain coatings having good surface properties.