The results of the investigation of some properties of polyethyleneterephtalate, phosphate glass and mica for the study of cluster decay and spontaneous fission of heavy nuclei are given. The investigation results of U-230 cluster decay and Ra-226 spontaneous fission investigation are presented. The probability of U-230 cluster decay in relation to alpha-decay is less than 7.5.10(14). The partial half-life of Ra-226 spontaneous fission is more than 6.6.10(17) yrs. The fusion-fission cross sections for the (Pb-208 + O-16 --> Th-224) reaction, as the inverse reaction of cluster decay, in the subbarrier region of ion energy was measured. For the energies of 78, 75, 73 and 68 MeV O-16 (lab.system) the cross-sections are 7.8; 3.7.10(-2) 8.5.10(-4) and 6.10(-6) mb, respectively.