Abstract: Catalytic systems particularly suitable for the polymerization of .alpha.-olefins containing from two to 20 carbon atoms, as well as for the copolymerization of ethylene with .alpha.-olefins containing from three to 20 carbon atoms, dienes, and cycloalkenes in processes wherein the catalyst is suspended in a solvent, in processes in gas phase, as well as in mass polymerization processes at high temperatures and pressures, are disclosed. The catalytic system is a mixture of a catalyst component A and a co-catalyst component B. The catalyst component A is formed by a functionalized inorganic porous oxide, by an organoaluminium compound and by an organometallic compound of a metal of the groups 3, 4, 5, or 6 of the periodic table. Functionalization of the inorganic oxide is by introduction of functional groups to be used to strongly fix the organoaluminium compound and the organometallic compound.