Abstract: Hyperbranched polyester of a polyol with 3 to 10 reactive hydroxyl groups, preferably of equivalent reactivity, and an aromatic polycarboxylic anhydride with 2 to 4 carboxyl groups, preferably 3 carboxyl groups, each hydroxyl group of the polyol forming an ester linkage with one anhydride group of the polycarboxylic anhydride, and further glycidyl (meth)acrylate or allyl glycidyl ether forming ester linkages with the remaining carboxyl groups of the anhydride and free hydroxyl groups. Further in the hyperbranched polyester (meth)acrylic anhydride and/or an aliphatic carboxylic anhydride form ester linkages with the free hydroxyl groups. The invention also comprises a process for the production of hyperbranched polyesters and such polyesters obtainable by the process. The hyperbranched polyesters can be used as resins, curable by UV irradiation, for the production of coatings, adhesives, laminates, foils and thin films and fibre-reinforced composites.