The invention relates to a thermoplastic molding material of an elastomeric polymer A, a shell B grafted to the polymer A, and a copolymer C as rigid matrix. The amount of polymer A is 1 to 25 percent by weight based on the weight of A+B+C. It has a glass transition temperature, Tg, of less than 0.degree. C. and an average particle size of 200 to 750 nanometers (d.sub.50 value of the integral mass distribution) and is composed of: 50 to 99.9 percent by weight of at least one alkylacrylate with 1 to 8 carbon atoms in the alkyl radical and 0.1 to 5 percent by weight of a polyfunctional monomer which has a crosslinking action. Grafting shell B represents 5 to 40 percent by weight based on A+B+C and is composed of at least one of the monomers of the group of(b.sub.1) vinylaromatic monomers, and(b.sub.2) the ethylenically unsaturated monomers.Grafting shell B is prepared in two stages with 30 to 70 percent by weight of the monomers b.sub.1 being used in the first stage, and 30 to 70 percent by weight of a mixture of monomers b.sub.1 and b.sub.2 in a weight ratio of 90:10 to 60:40 being used in the second stage.Copolymer C is added in an amount of 35 to 94 percent by weight based on A+B+C and consists of a vinylaromatic monomer and an ethylenically unsaturated monomer.The molding material may contain commonly used additives in effective amounts and is used for the preparation of molded parts.