The segmented and block copolymers of poly(L-lactide-co-p-dioxanone)(PDO) and L-lac-tide were prepared successfully by ring-opening polymerization in the presence of lauryl alcohol with stannous octoate catalyst. The products were characterized by SEM, $^1$H-NMR, $^{13}$ C-NMR, and scanning electron microscopy. The hydrolytic degradation of copolymers was studied in a phosphate buffer solution at pH=7.4 and 37$^{circ}C$. The degradation behavior was evaluated by analyzing the morphological changes. The weight loss, pH, and inherent viscosity changes suggested diffusion of low molecular weight chain segments into the reaction medium as a consequence of the cleavage of ester bonds On the material. Surface morphological changes observed using SEM suggest a heterogeneous degradation mechanism.