A solid component for catalysts for polymerizing alpha-olefins, comprising at least on the surface, the reaction product of a Mg dihalide with a halogenated tetravalent Ti compound selected from the group consisting of Ti tetrahalides and Ti halogen alcoholates and with a hydrocarbyl electron-donor capable of forming complexes with Mg dihalides, the molar ratio electron-donor/Ti in said product being higher than 0.2 and the molar ratio halogen atoms/Ti being comprised between 10 and 90, said component being further characterized in that at least 80% by weight of the tetravalent Ti compounds contained therein is insoluble in boiling n-heptane and in that at least 50% by weight of the Ti compounds insoluble in n-heptane is insoluble in TiCl.sub.4 at 80.degree. C., and also in that the surface area of the product insoluble in TiCl.sub.4 at 80.degree. C., and the surface area of said component as such, is higher than 40 m.sup.2 /g.