In the case of Ziegler catalysts based on a metallocene as the transition metal component and an aluminoxane as the activator, preactivation of the metallocene with the aluminoxane results in a considerable increase in the activity of the catalyst system. Furthermore, 1-olefin polymers of a high degree of isotacticity and having compact, spherical particles, a very narrow particle size distribution and a high bulk density are obtained by means of a catalyst system of this type.