High molecular weight polyphenylene ethers are prepared from monohydric phenols by an oxidative coupling reaction with oxygen in the presence of a catalyst complex obtained from a copper salt and an organic amine by a method wherein the metal component of the catalyst is separated off, after the polymerization, by the addition of a polymeric polycarboxylic acid which is essentially composed of unsaturated monofunctional or difunctional carboxylic acids and/or their anhydrides.Advantageously, the polymeric polycarboxylic acids used are homopolymers or copolymers of (a) from 50 to 100% by weight of one or more unsaturated monofunctional acids of 3 to 10 carbon atoms and/or one or more difunctional acids or their anhydrides of 4 to 6 carbon atoms and from 0 to 50% by weight of one or more monomers which do not possess an acid function and can be copolymerized with (a).