A facile route toward alternating polycarbonates by anionic copolymerization of carbon dioxide (CO,) and cyclohexene oxide (CHO), using lithium halide or alkoxide as initiators and triisobutylaluminum (TiBA) as activator, is reported. alpha,omega-Heterobifunctional and alpha,omega-dihydroxypoly(cydohexene carbonate)s (PCHC) as well as poly(CHC-co-CHO) copolymers with different carbonate composition could also be easily synthesized by adjusting the amount of TiBA or by adding inert lithium salts. The value of this initiating system also resides in the easy access to PSt-b-PCHC (PSt: polystyrene) and PI-b-PCHC (PI: polyisoprene) block copolymers which can be derived by mere one-pot sequential addition of styrene or dienes first and then of CO, and CHO under the same experimental conditions.