Rayleigh and Hyper-Rayleigh scatterings(HRS) from the nano-particle SnO2 were measured. It is found that as the concentration of the colloidal SnO2 or radiation power increases, the first- and second-order polarizabilities decrease. The radiation power dependencies of the first- and second-order polarizabilities show two domains: in high radiation power domain, the first- and second-order polarizabilities are approximately constant, in low radiation power domain, the first- and second-order polarizabilities increase sharply and become sensitive to the radiation power. The behavior of the concentration dependencies of the first- and second-order polarizabilities of colloidal SnO2 particles is similar to that of the radiation power dependence. A detailed mechanism explaining these phenomena has been discussed. The is the concentration of the colloidal SnO2 or radiation power increases, the first- and second-order polarizabilities decrease. The radiation power dependencies of the first- and second-order polarizabilities show two domains: in high radiation power domain, the first- and second-order polarizabilities are approximately constant, in low radiation power domain, the first- and second-order polarizabilities increase sharply and become sensitive to the radiation behavior. The behavior of the concentration dependencies of the first- and second-order polarizabilities of colloidal SnO2 particles is similar to that of the radiation power dependence. A detailed mechanism explains that these phenomena have been discussed.