The present invention relates to a process for the production of polyarylene ether block copolymers comprising, in a first stage, the reaction of at least one aromatic dihydroxy compound comprising 4,4′-dihydroxybiphenyl in a molar excess and of at least one aromatic dihalogen compound, to form a polybiphenyl sulfone polymer, and then, in a second stage, the reaction of the polybiphenyl sulfone polymer with at least one aromatic dihydroxy compound and of at least one aromatic dihalogen compound.The invention further relates to the resultant polyarylene sulfone block copolymers and to the use of the polyarylene sulfone block copolymers for the production of moldings, fibers, films, or foams.