Biodegradable polyesters based onA) 95-99.99 mol % of at least one polyester A containing as monomeric building blocks of an acid component comprisinga.sub.11) 20-95 mol % of at least one aliphatic or cycloaliphatic dicarboxylic acid or its ester-forming derivative anda.sub.12) 5-80 mol % of at least one aromatic dicarboxylic acid or its ester-forming derivative and at least one dihydroxy compound or at least one amino alcohol or their mixtures, andB) 0.01-5 mol % of a mixture comprising mono-, bi-, tri-, tetra- and higher-nuclear isocyanurates or corresponding compounds containing two, three or four functional groups capable of reacting with the end groups of polyester A, or mixtures of the isocyanurates and the corresponding compounds,as well as molding compositions comprising said polyesters, their manufacture and their use in the manufacture of moldings, filsm, fibers and coatings.