Process for the production of asymmetric, star-branched block copolymers which comprise, incorporated into the polymer, from 60 to 95% by weight of vinylaromatic and from 40 to 5% by weight of a conjugated diene having from 4 to 5 C atoms, based on the branched block copolymer, via sequential anionic polymerization and subsequent coupling of the resultant living block-copolymer anions by a coupling agent, and also vinylaromatic-diene block copolymers obtainable via the process and use of these for moldings and for thermoforming foils.