The present invention relates to a process for the production of low-halogen-content polybiphenyl sulfone polymers, to the resultant polybiphenyl sulfone polymers, to polybiphenyl sulfone polymers having less than 400 ppm content of polymer-bonded halogen, to thermoplastic molding compositions comprising these polybiphenyl sulfone polymers, and to their use for the production of moldings, of fibers, of films, of membranes, or of foams.