Abstract: Method of metathetical polymerization and copolymerization of cycloalkenes of norbornene type in the presence of catalytic system which is comprised ofa) a catalytic precursor prepared by reaction of a tungsten compound containing at least one atom of chlorine, bromine and/or iodine with sterically hindered amines, whereby concentration of the tungsten is 0.01 to 50 milimols per mol of monomer and molar ratio of tungsten/amine is 0.01 to 1:5,b) cocatalyst selected from the group of organic compounds of aluminium, tin, lead, silicon, lithium, magnesium, boron, zinc or germanium, whereby molar ratio tungsten/cocatalyst is 1:1 to 1:20 and possibly,c) moderator of the polymerization reaction selected from the group of ethers, esters, ketons or nitriles in mole ratio cocatalyst/moderator 1:1 to 1:10.