Abstract: The invention relates to a curable composition containing as component A) compounds with at least two activated double bonds (I), these being .alpha.,.beta.-unsaturated carbonyl compounds, .alpha.,.beta.-unsaturated carboxylic acid esters or .alpha.,.beta.-unsaturated nitriles, and compounds B) which contain at least two active hydrogen atoms or at least two groups with active hydrogen atoms or at least one active hydrogen atom and at least one group with an active hydrogen atom, and customary additives, catalysts, if appropriate pigments and an organic solvent. Either component A) or B) or components A) and B) are based on a branched soluble acrylate copolymer (P) which is obtainable by copolymerization ofa) 3 to 30% by weight of monomers with at least two ethylenically unsaturated polymerizable double bonds,b) 5 to 60% by weight of monomers with a functional group andc) 5 to 92% by weight of other ethylenically unsaturated monomers,the sum of a), b) and c) being 100% by weight.