The present invention relates to thermoplastic molding compositions comprising the following components: (A) at least one polyarylene ether, (B) at least one hyperbranched polymer selected from hyperbranched polycarbonates and hyperbranched polyesters, (C) optionally at least one fibrous or particulate filler, and (D) optionally further additives and/or processing aids. The present invention further relates to a process for producing the thermoplastic molding compositions of the invention, to their use for producing moldings, fibers, foams, films, or membranes, and to the resultant moldings, fibers, foams, films, and membranes.