The article describes two types of organoaluminate compounds which can serve as cocatalysts for metallocene complexes in alkene polymerization reactions: (a) sterically hindered arylaluminates, oligomeric compounds containing [Al(OPh)-O] units where Ph are aryl groups substituted in the second and the sixth positions with bulky alkyl or aryl groups; and (b) alkylaluminates, compounds containing [Al(OR)-O] units where OR is a heavily sterically hindered alkoxy group. The most effective substituents Ph in the arylaluminates are phenyl groups with two ortho-positioned tert-butyl or phenyl groups. The most effective substituent R in the alkylaluminates is CPh3. These cocatalysts can be produced via two alternative routes: (1) a reaction between an alkylalumoxane and a sterically hindered phenol or an alcohol or (b) two consecutive reactions: first, a reaction between a trialkylaluminum compound and a sterically hindered phenol or an alcohol and, second, a reaction between the product of the first step and water. Oligomeric cocatalyst compositions containing units of two types, organoaluminate and alkylalumoxane, also can serve as cocatalysts for metallocene complexes.