The constant molar flow (CMF) method has been successfully applied to measure equilibrium and dynamic parameters in porous adsorbent particles. However, the application of this method is confined to a linear system without the external film resistance. The aim of the present study is two-fold: to derive the exact analytical solution of the linear CMF model with the external film resistance and to extend the theory of the CMF model to the nonlinear system. As time becomes sufficiently large, the solution of the linear CMF model asymptotes to a straight line, of which the slope is a function of the equilibrium parameters only and the intercept is a function of the dynamic parameters such as the effective diffusivity and the external film mass transfer coefficient. On the contrary, the solution of the nonlinear CMF model has two asymptotes: the early time asymptote and the late time asymptote. Numerical analysis using the orthogonal collocation in the radial domain of the particle phase is also used to interpret the behavior of the nonlinear CMF model.