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 titanium, magnesium, chlorine and a benzenecarboxylic acid derivative, (2) an aluminum component and (3) a silane component. In the process, a titanium component (1) is employed which is obtained by (1.1) first preparing (I) a carrier from (Ia) a silica gel which has a relatively high moisture content, (Ib) an organomagnesium compound and (Ic) a gaseous chlorinating agent by a method in which (1.1.1) first (Ia) is reacted with (Ib), (1.1.2) then (Ic) is passed into the mixture obtained in (1.1.1), 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 derivative 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 or a titanium tetrachloride/hydrocarbon mixture, and (1.4) finally the solid-phase product resulting from (1.3) is washed with a liquid hydrocarbon.