Process for the polymerization of alpha -olefins under polymerization conditions in the presence of a transition metal complex and an activator, in which the transition metal complex is a complex according to the formula (I): COTxMLyAz where: M = a transition metal from groups 3-6 of the Periodic System of the Elements COT = a cyclooctatetraene ligand (C8R'8) and R' = a substituent; L = an anionic pi-bound ligand; A= a neutral ligand; y = the valency of M-(2*x); x = a number larger than or equal to 1/2, divisible by 1/2; and z = an integer larger than or equal to 0; and wherein the activator is a neutral Lewis acid or an ion complex.
