1.The polymerization of 1-methyl-1,5-cyclooctadiene using metathesis catalysts proceeds with opening of the ring exclusively at the unsubstituted double bond.2.We were the first to polymerize 3-methylcyclooctadiene and dimethyl-1,5-cyclooctadiene (mixture of 3,7- and 3,4-isomers) with opening of the ring to respectively give 1,4-polypiperylene and the alternating copolymer of piperylene with budadiene.3.The reaction of 1-methyl-1,5-cyclooctadiene with WCl6in the absence of cocatalysts leads to the formation of active centers, which are capable of initiating the polymerization of cycloolefins with opening of the ring.