A novel class of aliphatic polyesters, and their derived copolyesters, have been developed. Beside their specific mechanical and thermal properties, the durability, in terms of biodegradability and photodurability, has been investigated. In particular, the polymers were submitted to natural and accelerated photo-ageing and an original methodology based on melt rheology has been applied to determine molecular changes upon UV weathering. Both scission and recombination reactions, which strongly compete as a function of the exposure time, were found to cause a strong evolution of the molecular structure. The results indicate that chemical structure and stereochemistry of the novel materials define the predominant process and the overall behaviour of the samples upon UV exposure. Moreover, the changes of the molecular structure, induced by UV irradiation, could have a significant role into the further biodegradability of the polymers. Therefore, while the relationships between structure and durability enable to design materials with desired well-adapted performances according to their final destination, the biodegradable character upon lifetime use is considered as really questionable and needs further studies.