The present invention relates to a catalyst system for olefin polymerization comprising an organic transition metal compound and, as cocatalyst, an ionic compound made up of anions of the formula (Ia), [Al(OR.sup.1).sub.4].sup.- (Ia) where the radicals R.sup.1 are identical or different and are each, independently of one another, a radical R.sup.2R.sup.3(CF.sub.3).sub.2, R.sup.2 is a carbon or silicon atom and R.sup.3 is hydrogen, C.sub.1-C.sub.20-alkyl, C.sub.1-C.sub.20-fluoroalkyl, C.sub.6-C.sub.20-aryl, C.sub.6-C.sub.20-fluoroaryl, C.sub.7-C.sub.40-arylalkyl, C.sub.7-C.sub.40-fluoroarylalkyl, C.sub.7-C.sub.40-alkylaryl, C.sub.7-C.sub.40-fluoroalkylaryl or an SiR.sup.4.sub.3 group, where R.sup.4 may be identical or different and is each C.sub.1-C.sub.20-alkyl, C.sub.1-C.sub.20-fluoroalkyl, C.sub.6-C.sub.20-aryl, C.sub.6-C.sub.20-fluoroaryl, C.sub.7-C.sub.40-arylalkyl, C.sub.7-C.sub.40-fluoroarylalkyl, C.sub.7-C.sub.40-alkylaryl or C.sub.7-C.sub.40-fluoroalkylaryl, and Lewis-acid cations or Bronsted acids as cations.In addition, the invention relates to the process for preparing such a catalyst system and to a process for the polymerization of olefins in which this catalyst system is used.