Process for the preparation of a thermoplastic moulding composition of 10 to 65% by weight of at least one graft polymer which is obtainable by emulsion polymerization of styrene and acrylonitrile in a weight ratio of 90:10 to 50:50, it being possible for all or some of the styrene to be replaced by .alpha.-methylstyrene or methyl methacrylate, in the presence of at least one rubber base, and the weight ratio of monomers employed to rubber polymer employed being 20:80 to 70:30, and 90 to 35% by weight of a copolymer of styrene and acrylonitrile in a weight ratio of 90:10 to 50:50, it being possible for all or some of the styrene to be replaced by .alpha.-methylstyrene or methyl methacrylate, wherein, to prepare the graft polymer, the grafting monomers and 0.05 to 1.00 part by weight (per 100 parts by weight of grafting monomer) of a mercaptan are added stepwise to the latex of the rubber base over a period of time, the part amount of the monomer added in each time interval .DELTA.t.sub.n+1 being 0.30 to 0.95 times the amount of monomer added in the preceding time interval .DELTA.t.sub.n at least in the first half of the period of time, and the total period of time comprising n time intervals where n=3 to 30, and each time interval .DELTA.t being 5 to 100 minutes long.