Abstract: Olefins are polymerized and copolymerized in the presence of a solid catalyst which contains an organometallic compound and a solid material having at the surface thereof catalytic complexes containing a divalent metal, halogen, oxygen and a transition metal having halogenated substituents. The solid material of the catalyst is obtained by reacting a liquid halogenated derivative of a transition metal, such as TiCl.sub.4 or VOCl.sub.3 with a solid support which is a oxygenated compound of a divalent metal and which is substantially anhydrous and also substantially free of hydroxyl groups; examples of such a solid support include calcium, magnesium and zinc oxides and oxygenated salts such as nitrates, sulfates and silicates and organic carboxylate salts including salts of mono- and acetates polycarboxylic acids.