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Nowadays, the isolation of radioactive waste (RW) from the biosphere is one of the main problems of nuclear industry. Following the requirements of radiation safety geological isolation of RW requires a multi-barrier safety system, and natural clays are considered to be one of the most promising components. Bentonite clays, whose properties are provided by the presence of smectite group minerals, are considered to be the most promising material. A lot of works are devoted to radionuclides interaction with bentonite clays and their components. In this work, Cs interaction with various aluminosilicates (smectite, kaolinite, illite, and zeolite) was compared. During this study we performed experiments with natural bentonite clays of different deposits: previously non-widely studied deposits from Russia (Khakassia, Dash-Salakhinskiy, Zyryanskiy) and Kazakhstan (Dinosaur) as well as widely studied samples MX-80 (USA), KunipiaF (Japan), FEBEX (Spain). The cesium sorption was studied in a wide range of concentrations (10-14-10-2 M) and pH (2-10). During the study significant differences in cesium behavior on the various samples were observed. Differences in sorption were especially evident at trace concentrations of cesium. Decrease in cesium sorption in the row illite-montmorillonite~zeolite-kaolinite in the whole range of studied concentrations was observed. Despite differences in structure, similar sorption dependencies were obtained for samples MX-80 and zeolite. For some bentonites (FEBEX, Zyryanskiy, Dinosaur, Dash-Salakhinskiy, and Khakassia deposits), 2 plateaus on sorption isotherms can be observed, which indicates the existence of different sorption sites. MX-80 and KunipiaF have a similar mineral composition, but only one sorption site can be found, and the sorption values are significantly lower. Significant differences were also observed for cesium sorption on samples Khakassia and Dinosaur that have similar mineral composition. Thus, the significant difference in Cs sorption on bentonite samples with similar composition should be noted. This may be due to the influence of the fine structure of the sample. The correlation between sorption of trace cesium concentrations and the clay layer charge distribution was revealed. The data obtained allowed us to carry out modeling that adequately describes the sorption of cesium on a large set of aluminosilicates in various conditions.