A process for the manufacture of homopolymers and copolymers of .alpha.-monoolefins by polymerizing the monomer or monomers at relatively low temperatures under relatively low pressures by means of a Ziegler-Natta catalyst comprising (I) a titanium chloride component and (II) an aluminumalkyl component, wherein the titanium chloride component (I) employed is obtained by exposing a conventional catalyst component consisting, or substantially consisting, of titanium trichloride or titanium tetrachloride, to a carbon dioxide atmosphere under specific conditions. Catalysts obtained from titanium chloride components (I) which have been treated in this way exhibit a relatively long induction period.