A polymerization system for ring opening polymerization of cycloolefins, comprising a catalyst nullMOX2L2null, a Lewis acid as co-catalyst, and a chain-transfer agent, 1 wherein (1) both X groups are the same halogen atom selected from the group consisting of Cl and Br, and both L groups are the same halogen atom as X; or (2) both of the X groups are the same halogen atom selected from the group consisting of Cl and Br, and both of the L groups are the same straight chain or branched alkyl group having 1-4 carbon atoms; or (3) both X groups are the same halogen atom selected from the group consisting of Cl and Br, and both L groups are the same straight chain or branched alkoxy group having 1-4 carbon atoms; or (4) both X groups are the same alkyl group having 1-4 carbon atoms, and both L groups are the same alkoxy group having 1-4 carbon atoms; or (5) one X group is a halogen atom selected from the group consisting of Cl and Br, and the other X group together with both L groups constitute a tridentate ligand; or (6) one X group is a straight chain or branched alkoxy group having 1-4 carbon atoms, and the other X group together with both L groups constitute a tridentate ligand.