The present invention relates to a process for preparing highly functional hyperbranched polyesters which comprises reacting a reaction solution comprising solvent and (a) one or more dicarboxylic acids or one or more derivatives thereof with one or more at least trifunctional alcohols (b) or one or more tricarboxylic acids or higher polycarboxylic acids or one or more derivatives thereof with one or more diols (c) or one or more tricarboxylic acids or higher polycarboxylic acids or one or more derivatives thereof with one or more at least trifunctional alcohols (d) or one or more di- or polyhydroxycarboxylic acids (e) or one or more hydroxydi- or hydroxypolycarboxylic acids or mixtures of at least two of the above reaction solutions in the presence of an enzyme at temperatures above 60.degree. C. and pressures above 500 mbar.