Kinetics of ethylene homopolymerization reactions and ethylene/1-hexene copolymerization reactions using a supported Ziegler-Natta catalyst was carried out over a broad range of reaction conditions. The kinetic data were analyzed using a concept of multicenter catalysis with different centers that respond differently to changes in reaction parameters. The catalyst contains five types of active centers that differ in the molecular weights of material they produce and in their copolymerization ability. In ethylene homopolymerization reactions, each active center has a high reaction order with respect to ethylene concentration, close to the second order. In ethylene/alpha-olefin copolymerization reactions, the centers that have poor copolymerization ability retain this high reaction order, whereas the centers that have good copolymerization ability change the reaction order to the first order. Hydrogen depresses activity of each type of center in the homopolymerization reactions in a reversible manner; however, the centers that copolymerize ethylene and alpha-olefins well are not depressed if an alpha-olefin is present in the reaction medium. Introduction of an alpha-olefin significantly increases activity of those centers, which are effective in copolymerizing it with ethylene but does not affect the centers that copolymerize ethylene and alpha-olefins poorly. To explain these kinetic features, a new reaction scheme is proposed. It is based on a hypothesis that the Ti-C2H5 bond in active centers has low reactivity due to the equilibrium formation of a Ti-C2H5 species with the H atom in the methyl group beta-agostically coordinated to the Ti atom in an active center.