Aspects of the invention relate to block copolymers having the properties of thermoplastic elastomers made of blocks on the basis of isobutene monomer units as the soft segment and blocks on the basis of oligoamides composed of at least two base units, each of which comprises an amino or a carbonyl group in the α, β, γ or δ position to each other or directly bound to each other, as the hard segment. Such block copolymers are suited for producing fibers, microfibers, and films.