Polymers of propene are prepared using a Ziegler-Natta catalyst system consisting of (1) a titanium component which is based on a finely divided, shape-imparting silica gel and contains, in addition to titanium, magnesium, chlorine and a benzenecarboxylic acid derivative, (2) an aluminum component and (3) a silane component. In this process, a titanium component (1) is used which is obtained by a method in which (1.1) first (I) a carrier is prepared from (Ia) a silica gel, (Ib) an alkanol, (Ic) an organomagnesium compound and (Id) a gaseous chlorinating agent by a procedure in which (1.1.1) first (Ia) is reacted with (Ib), (1.1.2) then the mixture obtained in (1.1.1) is combined with (Ic), (1.1.3) then (Id) is passed into the mixture obtained in (1.1.2) and (I) is isolated, (1.2) thereafter a solid-phase intermediate is prepared from (I), (II) an alkanol, (III) titanium tetrachloride and (IV) a phthalic acid drivative by a procedure in which (1.2.1) first (I) is reacted with (II), (1.2.2) then (III) is introduced into the mixture resulting from (1.2.1), with the proviso that (IV) is also introduced during (1.2.1) and/or (1.2.2), (1.3) then the solid-phase product resulting from (1.2) is extracted with titanium tetrachloride and (1.4) finally the solid-phase product resulting from (1.3) is washed with a liquid hydrocarbon.