A theoretical approach to the kinetics of adsorption on the expanding interface of a micellar surfactant solution is proposed. The nonlinear partial differential equations of mass transfer of the micelles and monomers are reduced to ordinary differential equations, which are solved numerically along with the nonlinearized adsorption isotherm as a boundary condition. Being more general, this theoretical approach is consistent also with the special case of small deviations from equilibrium widely used in the kinetics of micellization. The theory is applied further to fit the experimental data for dynamic surface tension of micellar solutions of sodium dodecyl sulfate and sodium polyoxyethylene-2 sulfate measured by the maximum bubble pressure (MBP) method. The expansion of the bubble surface is accounted for by using the experimental dependence of the bubble size on time. The calculated effective rate constant of micelle decay for sodium dodecyl sulfate turns out to be sensitive to the mechanism of the micelle’s disintegration. This provides a possibility for one to determine the rate constants of the fast and slow processes in the relaxation kinetics of micellization by using a relatively simple experimental technique for dynamic surface tension measurement like the MBP method.