Block copolymers of (R,S)-beta-butyrolactone and epsilon-caprolactone have been synthesized by combining the anionic polymerization of the first monomer with the coordinative ring-opening polymerization of the second one. The copolymerization yield is close to 100% and the final molecular weight of each sequence can be predicted from the initial monomer-to-initiator molar ratio. The molecular weight distribution of copolymers obtained is quite narrow (M-w/M-n less than or equal to 1.3). According to NMR and DSC analysis, the polybutyrolactone block is atactic and totally amorphous, in contrast to the polycaprolactone block; which is semicrystalline. A partial miscibility df the two blocks in the amorphous phase has however been detected. Thermal and enzymatic degradations of the block copolymers’ have been investigated. The enzymatic degradation rate promoted by the lipase form Rhizopus arrhizus strongly depends on the copolyester composition and increases with the beta-butyrolactone content.