Linear block copolymers are disclosed. The polymers comprise a plurality of alternating polymeric blocks of amorphous copolymers of L-lactide and D-lactide with semicrystalline blocks of either L-lactide homopolymer or D-lactide homopolymer. The molecular weight can be built up by either of two techniques. The first technique is to use a chain extending agent such as a diacyl chloride or a diisocyanate to link a plurality of the preformed block copolymers. The second technique is to polymerize additional alternating amorphous and semicrystalline onto the original alternating block copolymers.