New highly active and highly stereospecific catalysts for the polymerization of alpha-olefins are disclosed, the starting components of which are(a) an organometallic-compound of Al free from halogen atoms bound directly to the Al atom;(b) an electron-donor compound (such as a Lewis base) in an amount such that 15% to 100% of the organometallic Al compound (a) is combined with the electron-donor compound; and(c) a solid component comprising, at least on the surface, the reaction product of a halogenated Mg compound with a tetravalent Ti compound and with an electron-donor compound, the molar ratio electron-donor compound/Ti being higher than 0.2, and the molar ratio halogen atoms/Ti being higher than 4.Processes for polymerizing the alpha-olefins and mixtures thereof with ethylene in contact with the new catalysts are also disclosed.