Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order, first-order (i. e, membrane diffusion), second-order, parabolic-diffusion, Elovich, two-constant equations, to the experimental data of Pb2+ and Cu2+ adsorption on variable charge soils and kaolinite. Assuming each M2+ occupied two adsorption sites, two more equations, the so-called surface second-order equation and third-order equation were derived and compared with the above equations according to the fitting results, which showed that the second-order equation and surface second-order equation, being one equation in different expressions under some conditions, were better than the other equations in describing the Pb2+ and Cu2+ adsorption kinetics, and the latter was the best. Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order, first- order, parabolic-diffusion, Elovich, two-constant equations, to the experimental data of Pb2 + and Cu2 + adsorption on variable charge soils and kaolinite. Assuming each M2 + occupied two adsorption sites, two more equations, the so- called surface second-order equation and third-order equation were derived and compared with the above equations according to the fitting results, which showed that the second-order equation and surface second-order equation, being one equation in different expressions under some conditions, were better than the other equation in describing the Pb2 + and Cu2 + adsorption kinetics, and the latter was the best.