Isobutylalumoxanes have been obtained by hydrolysis of triisobutylaluminium (TIBA) with water in the form of vapour (1) or ice particles (2) at Al-TIBA/H2O = 2 mol/mol. H-1 NMR spectra of hydrolyzates showed the presence of unreacted TIBA indicating the formation of alumoxanes larger than (Bu2Al)-Bu-i-O-Ali- Bu-2 which one can expect based on the molar ratio of reagents. Alumoxanes 1 and 2 demonstrate high activating ability for rac-Et(2-MeInd)(2)ZrMe2 in copolymerization reactions of ethylene with propylene and terpolymerization of ethylene with propylene and 5-ethylidene-2-norbornene. Alumoxane 1 demonstrates high structural and chemical stability during long-term storage (for 1 year) that results in consistent activating ability and similarity of molecular weight characteristics of polymer formed. Alumoxane 2 is much less structurally stable which is manifested in considerable changes of H-1 NMR spectra of the product even after several days of storage. It essentially loses activating ability after 3 months' storage. The alumoxanes with high activating ability have been also obtained by in situ TIBA hydrolysis with water intentionally incorporated into toluene (similar to 1 x 10(-2) mol/l) prior to polymerization also at Al-TIBA/H2O = 2 mol/mol. The differences of catalytic systems with different activators are also reflected in differences in microstructure, molecular-weight, thermal-physical characteristics and physicalmechanical properties of copolymers formed.