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The book described catalytic systems for living polymerization of 1,3-butadiene by CoX2 ( X = Halogens ) combined with MAO as a cocatalyst at 0, 10 and 18 C. The uni-modal molecular weight distribution curves of the resulting polymers shifted toward higher molecular weight regions and became narrower with the increasing of the polymerization time. The number-average molecular weight increased linearly against polymerization time, while the polymer yield exponentially increased in the initial stage. As a consequence, the number of polymer chains calculated from the polymer yield and Mn value increased gradually with polymerization time to reach a steady value. These phenomena were interpreted based on a slow initiation system without any termination and chain transfer reaction. The kinetic analysis indicated that the rates of initiation were significantly influenced by the nature of the halides and descended in the following order, CoCl2 CoBr2CoI2CoF2 = 0, while the rates of propagation were independent on variation of halogen ligands. The effects of other cocatalysts and additive on livingness were also analyzed systematically.