The present invention is generally directed to a process for producing lactide-based polymers and the polymers produced by this process. The polymers of the present invention are terpolymers formed by the copolymerization of a lactide monomer, a linking monomer and an epoxy-terminated monomer. In one embodiment of the invention, the polymers may be formed from fluorine-containing monomers or aromatic ring-containing monomers. The disclosed materials may display improved hydrolytic and thermal characteristics as compared to previously known lactide-based materials. For example, the lactide based terpolymers may have a glass transition temperature over 60° C. For instance, lactide-based thermoplastic terpolymers of the present invention can have a glass transition temperatures of about 80° C. or higher. Lactide-based thermoset networks of the invention can have glass transition temperatures of up to about 200° C.