Synthetic biodegradable polymers are of great interest for biomedical applications such as surgical sutures and drug delivery systems. The copolymers of ${alpha}-amino$ acids and ${alpha}-hydroxy$ matrices having the required permeability for drugs. Poly (glycine.co-lactic acid) and poly (glycine-co-glycolic acid) have been synthesized by ring-opening polymerization. Morpholine-2, 5-diane, lactide, and glycolid have been used as starting materials for polydepsipeptides. The synthesized monomers and copoylmers have been identified by NMR and FT-lR spectrophotometer. The thermal properties and glass transition temperatures ($T_g$) of the copolymers have been measured by differential scanning calorimetry. The $T_g$ values of poly (glycine-co-lactic acid) and poly (glycine co.glycolic acid) are increased with increasing mole fraction of morpholine-2, 5-dione in the copolymers.