The catalyst systems comprise as active constituents a) a titanium-containing solid component comprising a compound of titanium, a compound of magnesium, a halogen, an inorganic oxide as support and a carboxylic ester as electron donor compound, and also, as cocatalyst, b) an aluminum compound and c) optionally a further electron donor compound, wherein the inorganic oxide used has a pH of from 1 to 6, an average particle diameter of from 5 to 200 &mgr;m, an average primary particle diameter of from 1 to 20 &mgr;M and voids or channels having an average diameter of from 0.1 to 20 &mgr;m and a macroscopic share of the volume of the overall particle within the range from 5 to 30%.