L,L-lactide (LA) and epsilon-caprolactone (CL) block copolymers have been prepared by initiating the poly (epsilon-caprolactone) (PCL) block growth with living poly(L,L-lactide) (PLA*). In the previous attempts to prepare block copolymers this way only random copolyesters were obtained because the PLA* + CL cross-propagation rate was lower than that of the PLA-CL* + PLA transesterification. The present paper shows that application of Al-alkoxide active centers that bear bulky diphenolate ligands results in efficient suppression of the transesterification. Thus, the corresponding well-defined di- and triblock copolymers could be prepared.