Synthetic zeolites differing in composition, framework parameters, and exchange cations that balance charges of aluminum-oxygen framework tetrahedra and natural finely divided clinoptilolite-containing tuffs have been used for heterogenization of metal complex catalysts. In the reaction of incomplete hydrolysis of alkylaluminum compounds with water contained on the surface and in the intracrystalline cavities of synthetic zeolites, bonded alkylalumoxanes have been synthesized and further used to create immobilized zirconocene olefin polymerization catalysts, close in activity to similar homogeneous Zr-cene systems, and heterogenized vanadium catalysts. Based on finely divided natural zeolites and ultrahigh-molecular-weight polyethylene, the following materials have been fabricated using the polymerization filling method: a composite that combines high wear-resistant properties with a low friction coefficient, has good strain-stress characteristics, and can be used for manufacturing friction units under load; an organomineral sorbent suitable for solving environmental problems associated with the treatment of natural water for the removal of cesium and strontium radionuclides, heavy metals, and ammonium.