Polyurethane-modified addition copolymers preparable by free-radically (co)polymerizing an olefinically unsaturated monomer (a) in an aqueous or nonaqueous medium comprising at least one reaction product (A/B) of(A) at least one addition copolymer containing on average per molecule at least 0.1 isocyanate-reactive functional groups and preparable by free-radical copolymerization of at least a) at least one olefinically unsaturated monomer and b) at least one olefinically unsaturated monomer different than the olefinically unsaturated monomer (a1) and of the general formula I R.sup.1R.sup.2C.dbd.CR.sup.3R.sup.4 (I) in which the radicals R.sup.1, R.sup.2, R.sup.3, and R.sup.4 each independently of one another are hydrogen atoms or substituted or unsubstituted alkyl, cycloalkyl, alkylcycloalkyl, cycloalkylalkyl, aryl, alkylaryl, cycloalkylaryl, arylalkyl or arylcycloalkyl radicals, with the proviso that at least two of the variables R.sup.1, R.sup.2, R.sup.3, and R.sup.4 are substituted or unsubstituted aryl, arylalkyl or arylcycloalkyl radicals, especially substituted or unsubstituted aryl radicals; in an aqueous medium or nonaqueous medium; and (B) at least one polyisocyanate; processes for preparing them, and their use.