Abstract: A method is disclosed for preparing a catalyst system for polymerizing .alpha.-olefins. This method comprises admixing with at least an organoaluminum compound an activated titanium component which is prepared by first reacting a titanium compound of the general formula, TiX.sub.n (OR).sub.4-n (in which X is a halogen atom, R is an alkyl group or a phenyl group, and n is 2 to 4), with a metal of Group II or III of the Periodic Table and a halide of a metal of Group II or III of the Periodic Table in the presence of an aromatic compound, then treating the resulting reaction product with an oxygen-containing organic compound, and further treating with a tetrahalide of titanium, vanadium or both at a temperature of from -80.degree. C. to 80.degree. C., and finally aging at a temperature above 30.degree. C. for from 30 minutes to 24 hours.