Copolymers I carrying functional groups and comprising a) 20-60 mol % of at least one monoethylenically unsaturated C4-C6-dicarboxylic acid or an anhydride thereof, b) 10-70 mol % of at least one oligomer of propene or of a branched 1-olefin of 4 to 10 carbon atoms, having an average molecular weight Mw of from 300 to 5000, and c) 1-50 mol % of at least one monoethylenically unsaturated compound which is copolymerizable with the monomers a) and b), a process for their preparation, oil-soluble reaction products obtainable therefrom by reaction with an amine and the use of said reaction products as additives for lubricants and fuels.