Thermoplastic molding compositions comprising A) a graft polymer comprising 1) an elastomeric graft core, obtainable by copolymerization of one or more C1-C10-alkyl acrylates, and a monomer with crosslinking effect, and 2) a graft shell comprising a styrene compound or a C1-C8-alkyl acrylate or methacrylate, or a mixture of the styrene compound and the C1-C8-alkyl acrylate or methacrylate, and B) a thermoplastic polymer comprising C) an elastomeric block copolymer in which all or virtually all of the olefinic double bonds have been hydrogenated, comprising at least one block A, which forms a hard phase and contains, in its polymer chain, units of a vinylaromatic monomer, and/or a block B, which forms a first elastomeric (soft) phase and contains diene monomers, and at least one elastomeric block B/A, which forms a soft phase, and contains, randomly in its polymer chain, units of both a vinylaromatic monomer and a diene, where the glass transition temperature Tg of the block A is above 25° C. and that of the block B/A is below 25° C. and the phase-volume ratio of block A to block B/A is chosen so that the proportion of the hard phase in the entire block copolymer is from 1 to 40% by volume and the proportion by weight of the diene is less than 50% by weight.