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), (R1)x—A—OH)y  (I) where A is an atom of group 13 or 15 of the Periodic Table, R1 are identical or different and are each, independently of one another, hydrogen, halogen, C1-C20-alkyl, C1-C20-haloalkyl, C1-C10-alkoxy, C6-C20-aryl, C6-C20-haloaryl, C6-C20-aryloxy, C7-C40-arylalky, C7-C40-haloarylalkyl, C7-C40-alkylaryl, C7-C40-haloalkylaryl or an OSiR32 group, where R2 are identical or different and are each hydrogen, halogen, C1-C20-alkyl, C1-C20-haloalkyl, C1-C10-alkoxy, C6-C20-aryl, C6-C20-haloaryl, C6-C20-aryloxy, C7-C40-arylalkyl, C7-C40-haloarylalkyl, C7-C40-alkylaryl or C7-C40-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.