The invention relates to a method for the purification of poly(arylene ethers) of formula (I) in which m=0 to 1.0, n=1.0-m, and Ar1, Ar2, Ar3 and Ar4 independently represent divalent arylene groups. The compound of formula (I) is produced in a first step 1, with a raw product being obtained by bringing a metal or ammonium salt of divalent dihydroxy derivatives of Ar1 or Ar3 into contact with one or more dihalogenated derivatives of Ar2 and/or Ar4, in the presence of a solvent LM1. A precipitate that is present, if appropriate, is separated (step B) so as to obtain a solution L which then undergoes a membrane filtration (step C).