Abstract: Catalyst systems of the Ziegler-Natta type comprise as active constituents a) a solid component comprising a compound of titanium or vanadium, a compound of magnesium, a particulate inorganic oxide as support and an internal electron donor compound, and as cocatalyst b) an aluminum compound and c) if desired, a further, external electron donor compound, wherein the particulate, inorganic oxide used has a specific surface area of from 350 to 1000 m2/g and a mean particle diameter {overscore (D)} in the range from 5 to 60 &mgr;m and comprises particles which are composed of primary particles having a mean particle diameter {overscore (d)} in the range from 1 to 10 &mgr;m and contain voids or channels between the primary particles, where the macroscopic proportion of voids or channels having a diameter of greater than 1 &mgr;m in the particles of the inorganic oxides is in the range from 5 to 30% by volume and the molar ratio of the compound of magnesium to the particulate, inorganic oxide is from 0.