The invention accordingly provides a continuous process for reacting synthetic poly(carboxylic acid)s (A) containing, per polymer chain, at least 10 structural repeat units of formula (I) where R1 is hydrogen, a C1- to C4-alkyl group or a group of formula -COOH, R2 is hydrogen or a C1- to C4-alkyl group, and R3 is hydrogen, a C1- to C4-alkyl group or -COOH, with alcohols (B) of general formula (II) R4-(OH)n (II) where R4 is a hydrocarbyl radical of 1 to 100 carbon atoms which may be substituted or which may contain hetero atoms, and n is a number from 1 to 10 by a reaction mixture containing at least one synthetic poly(carboxylic acid) (A) and at least one alcohol of formula (II) in a solvent mixture containing water and, based on the weight of the solvent mixture, 0.1 - 75% by weight of at least one water-miscible organic solvent, and wherein the organic solvent has a dielectric constant of at least 10 when measured at 25 DEG C, being introduced into a reaction sector and on flowing through the reaction sector being exposed to microwave radiation, and wherein the reaction mixture in the reaction sector is heated by the microwave irradiation to temperatures above 100 DEG C.