Thermoplastic molding materials contain(A) from 5 to 95% by weight of a nylon and(B) from 5 to 95% by weight of a copolymer composed of(B.sub.1) from 50 to 99.9% by weight of a styrene of the general formula I ##STR1## where R.sup.1 is alkyl or 1 to 4 carbon atoms or hydrogen, R.sup.2 is alkyl of 1 to 6 carbon atoms or halogen and m is 0, 1, 2 or 3,(B.sub.2) from 0.1 to 30% by weight of a monomer containing epoxide groups (II) ##STR2## or of a monomer containing lactam groups (III) ##STR3## or of a monomer containing halobenzyl groups (IV) ##STR4## where R.sup.3 is a divalent, branched or straight-chain alkyl group of 2 to 15 carbon atoms, R.sup.4 is alkyl of not more than 6 carbon atoms, X is halogen, n is 1, 2 or 3 and r is 0, 1, 2 or 3, and(B.sub.3) from 0 to 48% by weight of further comonomers.