Elastomeric block copolymers having star-shaped molecular architecture, where the star-shaped molecular architecture has at least two different arms of the star, a process for producing the elastomeric block copolymers, the use of the elastomeric block copolymers for producing moldings, or as adhesive layer in multilayer foils; as seal; as adhesion promoter or thermoplastic component in wood-plastics composites; as hot-melt adhesive component; for impact-modifying thermoplastics or elastomers, or for compatibilization, and to foils, foams, thermomoldings, injection moldings, flexible tubing, or profile extrudates composed of at least one elastomeric block copolymer.