Abstract: A transparent thermoplastic molding material contains, based on A+B,A: from 5 to 95% by weight of polystyrene andB; from 95 to 5% by weight of a nonelastomeric star block copolymer which is composed of, based on B, b.sub.1 from 60 to 95% by weight of styrene and b.sub.2 from 5 to 40% by weight of one or more conjugated dienes of 4 or 5 carbon atoms and is prepared in a conventional manner by sequential anionic polymerization using one or more organolithium compounds as an initiator and in the presence of a solvent with subsequent coupling.In this process, component A is produced by conventional anionic polymerization using one or more organolithium compounds in the presence of an organic solvent.The molding material is prepared by mixing the components A and B, with or without C, in a conventional manner and is used for the production of moldings.