Disclosed are catalyst components for the polymerization of olefins which include magnesium halide in active form, and, supported thereon, a titanium halide or titanium halogen alcoholate and an electron-donor compound selected from the group diamines of formula ##STR1## wherein the radicals R.sub.1 to R.sub.10 are the same or different and are hydrogen or C.sub.1 -C.sub.18 hydrocarbon radicals, with the proviso that at least one of the R.sub.7 and R.sub.8 radicals and at least one of the R.sub.9 and R.sub.10 radicals are not hydrogen. Also, disclosed are catalysts obtained from the catalyst components and an Al-alkyl compound, as well as catalysts obtained by reaction of an Al-alkyl compound and a diamine of formula (I) with a solid catalyst component including a titanium halide or a titanium halogen alcoholate, and an electron-donor compound having particular characteristics of extractability with Al-triethyl, supported on magnesium halide in active form.