The present invention relates to new biodegradable polymers. These polymers comprise biodegradable polyester-based prepolymers, to which ring-structured anhydrides which have different hydrophobicities have been connected, and which are either coupled to form linear thermoplastic polyester anhydrides or cross-linked to form network-structured polyester anhydrides. It is possible to adjust widely the degradation rate and mechanism of the polymers according to the present invention, and thus they can be used, for example, in the controlled dosing of pharmaceutical ingredients, for tissue technological applications, in surgery and in bioactive composites.