A biodegradable polyester obtainable by reacting a mixture comprising (a1) from 95 to 99.9% by weight of a polyester P1 obtainable by reacting a mixture essentially comprising (b1) a mixture comprising 35-95 mol % of adipic acid or ester-forming derivatives thereof, 5-65 mol % of terephthalic acid or ester-forming derivatives thereof, and 0-5 mol % of a compound containing sulfonate groups, and (b2) a dihydroxy compound selected from the group consisting of C.sub.2 -C.sub.6 -alkanediols and C.sub.5 -C.sub.10 -cycloalkanediols, with the proviso that a compound D with at least three groups capable of ester formation is employed to prepare the polyester P1, (a2) from 0.1 to 5% by weight of a divinyl ether C1 and (a3) from 0 to 5 mol %, based on component (b1) from the preparation of P1, of compound D, and other biodegradable polymers and thermoplastic molding compositions, processes for the preparation thereof, the use thereof for producing biodegradable moldings and adhesives.