Ethylene is homopolymerised or copolymerised by means of a Ziegler catalyst system comprising (1) a transition-metal catalyst component, (2) an organoaluminium catalyst component and (3) an organohalogen catalyst component, where (1) is the solid-phase product (IV) obtained by (1.1) first (1.1.1) combining an inorganic oxide (I) as support material and (1.1.2) a solution (II) of (IIa) a certain oxahydrocarbon and (IIb) a transition-metal starting component to form a suspension (III), evaporating this suspension to form a solid-phase intermediate (IV), and (1.2) then (1.2.1) combining the intermediate (IV) obtained from (1.1) and (1.2.2) a dissolved organoaluminium compound (V) to form a suspension, the resultant solid-phase product (IV) as the suspended material being the transition-metal catalyst component (1), wherein (1) is prepared using, as (IIb), exclusively a vanadium trichloride/alcohol complex.
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