A 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, characterized in that a1) in a first reactor, from 30 to 75% by weight of vinylaromatic, based on the entire vinylaromatic content of the hyperbranched block copolymer, are polymerized to completion in the presence of an initiator la to give vinylaromatic-block anions Sa with molar mass Mw from 40 000 to 250 000 g/mol; a2) from 5 to 60% by weight of diene, based on the entire diene content of the branched block copolymer, are then added to the vinylaromatic-block anion Sa and polymerized to completion to give a block-copolymer anion SaB1 having a diene block B1; b) separately in another reactor, in the presence of an initiator Ib, from 25 to 70% by weight of vinylaromatic are subjected to single or multiple initiation and are polymerized to completion to form one or more vinylaromatic-block anions Sb1 to Sbn+1 with molar mass Mw from 5000 to 50 000 g/mol; c) the anionic blocks SaB1 and Sb1 to Sbn+1 obtained in a2) and b) are combined in a reactor; d) the remaining quantity of diene, based on the entire diene content of the branched block copolymer, is added to this mixture and polymerized to completion to give block-copolymer anions SaB1 B2 and, respectively, Sb1 B2 to Sbn+1 B2 comprising diene blocks B2; and e) the resultant block-copolymer anions are coupled by a di- or polyfunctional coupling agent to give a branched block copolymer. a1) in a first reactor, from 30 to 75% by weight of vinylaromatic, based on the entire vinylaromatic content of the hyperbranched block copolymer, are polymerized to completion in the presence of an initiator la to give vinylaromatic-block anions Sa with molar mass Mw from 40 000 to 250 000 g/mol; a2) from 5 to 60% by weight of diene, based on the entire diene content of the branched block copolymer, are then added to the vinylaromatic-block anion Sa and polymerized to completion to give a block-copolymer anion SaB1 having a diene block B1; b) separately in another reactor, in the presence of an initiator Ib, from 25 to 70% by weight of vinylaromatic are subjected to single or multiple initiation and are polymerized to completion to form one or more vinylaromatic-block anions Sb1 to Sbn+1 with molar mass Mw from 5000 to 50 000 g/mol; c) the anionic blocks SaB1 and Sb1 to Sbn+1 obtained in a2) and b) are combined in a reactor; d) the remaining quantity of diene, based on the entire diene content of the branched block copolymer, is added to this mixture and polymerized to completion to give block-copolymer anions SaB1 B2 and, respectively, Sb1 B2 to Sbn+1 B2 comprising diene blocks B2; and e) the resultant block-copolymer anions are coupled by a di- or polyfunctional coupling agent to give a branched block copolymer. b) separately in another reactor, in the presence of an initiator Ib, from 25 to 70% by weight of vinylaromatic are subjected to single or multiple initiation and are polymerized to completion to form one or more vinylaromatic-block anions Sb1 to Sbn+1 with molar mass Mw from 5000 to 50 000 g/mol; c) the anionic blocks SaB1 and Sb1 to Sbn+1 obtained in a2) and b) are combined in a reactor; d) the remaining quantity of diene, based on the entire diene content of the branched block copolymer, is added to this mixture and polymerized to completion to give block-copolymer anions SaB1 B2 and, respectively, Sb1 B2 to Sbn+1 B2 comprising diene blocks B2; and e) the resultant block-copolymer anions are coupled by a di- or polyfunctional coupling agent to give a branched block copolymer.