The thermoplastic molding composition comprises a) as component A, from 3 to 78% by weight of one or more styrene copolymers which have no units derived from maleic anhydride, b) as component B, from 15 to 90% by weight of one or more polyamides, c) as component C, from 5 to 50% by weight of one or more impact-modifying graft rubbers without olefinic double bonds in the rubber phase, d) as component D, from 1 to 25% by weight of one or more styrene copolymers which have, based on the entire component D, from 0.5 to 5% by weight of units derived from maleic anhydride, e) as component E, from 1 to 30% by weight of one or more further rubbers based on olefinic monomers without core-shell structure, and having at least 0.1% by weight of functional monomers, f) as component F, from 0 to 50% by weight of one or more fibrous or particulate fillers, g) as component G, from 0 to 40% by weight of further additives, where the entire amount of components A to E and, if appropriate, F and G is 100% by weight.