Abstract: Low or medium-density straight-chain ethylene polymers are prepared by copolymerising ethylene with a C.sub.4 -C.sub.6 alpha-olefin at elevated temperature and pressure in a tubular reactor and in the presence of a Ziegler-type catalyst comprising a trialkyl aluminium as co-catalyst and a solid component, the solid component being obtained:by spray-drying an ethanolic solution of magnesium chloride to obtain a solid substrate of magnesium chloride particles containing alcoholic hydroxyls,by reacting the substrate with titanium tetrachloride to form an activated substrate, andby reacting the activated substrate with an alkyl aluminium chloride to chlorinate the titanium and partially or completely reduce the titanium from the tetravalent to the trivalent state.