A thermoplastic molding material consists of a polycarbonate A and a graft copolymer B, the latter consisting of an elastomer (rubber) (b.sub.1) and a shell (b.sub.2) grafted onto the elastomer.The elastomer (b.sub.1) contains, as copolymerized units, from 35 to 100% by weight of a diene from the group consisting of the conjugated dienes of 4 to 5 carbon atoms, and can contain, as copolymerized units, from 0 to 65% by weight of a monomer from the group consisting of the alkyl acrylates or alkyl methacrylates, where alkyl is of 1 to 8 carbon atoms.The shell (b.sub.2) is obtained in a conventional manner by successive polymerization of the monomers constituting the shell, in two process steps, in the presence of the elastomer (b.sub.1); in a first process step, from 10 to 90% by weight of a mixture of a vinylaromatic hydrocarbon and one or more ethylenically unsaturated monomers which differ from the said hydrocarbon, in a weight ratio of from 90:10 to 60:40, are first incorporated as copolymerized units, followed by the polymerization of from 90 to 10% by weight of a monomer from the group consisting of the alkyl acrylates or of the alkyl methacrylates, where alkyl is of 1 to 8 carbon atoms.The molding material is used for the production of shaped articles.