Thermoplastic molding materials preparedA) from 35 to 99.5% by weight of a matrix copolymer (A) ofa.sub.1) from 50 to 95% by weight of styrene and/or .alpha.-methylstyrene,a.sub.2) from 5 to 50% by weight of acrylonitrile anda.sub.3) from 0 to 20% by weight of further comonomersB) from 0 to 50% by weight of a particulate graft copolymer (B) which is insoluble in (A), has a median particle diameter of from 0.03 to 1 .mu.m and preparedb.sub.1) from 30 to 80% by weight of a core comprising an elastomeric polymer having a glass transition temperature of less than -10.degree. C. andb.sub.2) from 20 to 70% by weight of a graft shell comprising a polymer which is compatible or partly compatible with (A)andC) from 0.5 to 30% by weight of a particulate crosslinked copolymer (C) which is insoluble in (A), has a median particle diameter of from 0.5 to 50 .mu.m and comprisesc.sub.1) from 50 to 89.95% by weight of styrene and/or .alpha.-methylstyrene,c.sub.2) from 10 to 50% by weight of acrylonitrile,c.sub.3) from 0.05 to 5% by weight of a polyfunctional, crosslinking monomer,c.sub.4) from 0 to 10% by weight of a monomer which contains acidic or basic groups andc.sub.5) from 0 to 20% by weight of further comonomers.