Aromatic polycondensates are prepared in a continuous process froma) aromatic hydroxy-, thio- and/or amino-carboxylic acids,b) aromatic dihydroxy-, dithio-, diamino- and/or hydroxy-amino compounds,c) urea as an optional component andd) a molar amount equivalent to the sum of components b) and c) of aromatic dicarboxylic acids,by1. reacting components a), b), d) and optionally c) with lower fatty acid anhydrides in excess at from 140.degree. to 280.degree. C. with distillative removal of fatty acids and fatty acid anhydrides,2. passing the oligomer mixture downward through a perpendicular precondensation zone to form a two-phase mixture of prepolymers and vaporous fatty acids,3. separating the prepolymers from the vaporous fatty acids and4. condensing the prepolymer in a condensation zone to give a granulable polycondensate.