The invention relates to thermoplastic molding compositions comprisingA) from 30 to 98% by weight of a graft copolymer comprisinga.sub.K) from 30 to 90% by weight of an elastomeric graft core,a.sub.S) from 10 to 70% by weight of a graft shell comprisinga.sub.S /1) from 50 to 100% by weight of a styrene compound or a C.sub.1 -C.sub.8 -alkyl acrylate or methacrylate, or a mixture thereof, anda.sub.S /2) from 0 to 50% by weight of one or more other monomers,B) from 1 to 50% by weight of a thermoplastic polymer andC) from 1 to 70% by weight of an elastomeric block copolymer prepared by anionic polymerization of the monomers with addition of a potassium compound soluble in non-polar solvents (Step 1) followed by hydrogenation of all or virtually all the olefinic double bonds of the polymer obtained in Step 1, as described in greater detail herein.