Production of aromatic polyethers by reacting (i) a mixture of a bisphenol and a dihalobenzenoid compound or (ii) a halophenol, in which dihalobenzenoid compound or halophenol the halogen atoms are activated by ortho or para --SO.sub.2 -- or --CO-- groups, with an alkali metal (bi)carbonate, wherein the reaction is carried out in the absence of a solvent and in the presence of an infusible particulate support substance, preferably inorganic or polymeric, yielding a reaction medium in the form of a free-flowing powder by the end of the reaction.