In block copolymers of the general formula A--B--A' which have a molecular weight of less than 300,000 and consist of from 18 to 40% by weight of a vinylaromatic hydrocarbon and from 60 to 82% by weight of one or more partially or completely hydrogenated hydrocarbons and in which A and A' are each a polymer block of a vinylaromatic hydrocarbon and B is a polymer block of a diene hydrocarbon, the weight ratio of the polymer blocks A to A' is less than or equal to 1:5 and greater than 1:10 and the mean molecular weight of polymer block A is from 2,000 to 20,000 and that of the polymer block A' is from 10,000 to 110,000 and the molecular weight of the B block is not less than 18,000. The block copolymers are prepared by a process in which, in a first polymerization stage, the vinylaromatic hydrocarbon is completely polymerized to form the A or A' block, in the second polymerization stage the diene hydrocarbon is completely converted to form the B block and thereafter the second portion of the vinylaromatic hydrocarbon is polymerized on to form the A or A' block, the portion of a vinylaromatic compound for the preparation of the A' block being not less than five times, and not more than 10 times, the weight used to form the A block. The block copolymers are used for the preparation of molding materials.