The present invention relates to polyarylene ether block copolymers according to the general formula A-K—X—K-A, where —X— is a polyarylene ether segment with number-average molar mass of at least 5000 g/mol, and A- is a segment of the general structure R2NH—(R1—NH—CO—Ar—CO—NH)n—R1—NH—, in which R1 is a linear or branched alkylene group having from 2 to 12 carbon atoms and Ar is an arylene group having from 6 to 18 carbon atoms, and R2 is selected from aryloyl, alkyloyl, and H, and in which the number average of n is from 1 to 3, and there is a coupling group K of the structure —CO—Ar3—CO— linking each A to X, in which Ar13 is an aromatic group having from 6 to 18 carbon atoms. The present invention also relates to a process for the production of the polyarylene ether block copolymers of the invention, to polymer compositions comprising the polyarylene ether block copolymers of the invention, and also to the use thereof for the production of moldings, of films, of fibers, or of foams.