The present invention relates to a process for preparing a supported cocatalyst for olefin polymerization, which comprises reactingA) a support bearing functional groups,B) triethylaluminum andC) a compound of the formula (I), (R.sup.1).sub.x--A--OH).sub.y (I) where A is an atom of group 13 or 15 of the Periodic Table, R.sup.1 are identical or different and are each, independently of one another, hydrogen, halogen, C.sub.1-C.sub.20-alkyl, C.sub.1-C.sub.20-haloalkyl, C.sub.1-C.sub.10-alkoxy, C.sub.6-C.sub.20-aryl, C.sub.6-C.sub.20-haloaryl, C.sub.6-C.sub.20-aryloxy, C.sub.7-C.sub.40-arylalky, C.sub.7-C.sub.40-haloarylalkyl, C.sub.7-C.sub.40-alkylaryl, C.sub.7-C.sub.40-haloalkylaryl or an OSiR.sub.3.sup.2 group, where R.sup.2 are identical or different and are each hydrogen, halogen, C.sub.1-C.sub.20-alkyl, C.sub.1-C.sub.20-haloalkyl, C.sub.1-C.sub.10-alkoxy, C.sub.6-C.sub.20-aryl, C.sub.6-C.sub.20-haloaryl, C.sub.6-C.sub.20-aryloxy, C.sub.7-C.sub.40-arylalkyl, C.sub.7-C.sub.40-haloarylalkyl, C.sub.7-C.sub.40-alkylaryl or C.sub.7-C.sub.40-haloalkylaryl, y is 1 or 2 and x is 3 minus y. In addition, the invention relates to supported cocatalysts obtainable by such a process, to the use of the supported cocatalysts for preparing a catalyst system for the polymerization of olefins, to catalyst systems for the polymerization of olefins obtainable from the supported cocatalysts and to a process for the polymerization of olefins in which these catalyst solids are used.