An analytical method has been developed for solving the partial differential equations that govern double‐stream diffusion under very general conditions. The diffusion coefficient of the slow stream is set equal to zero. The trapping and releasing rates and the diffusion coefficient of the fast stream are assumed to be functions of distance and time rather than constants. General solutions of the equations which satisfy the boundary and initial conditions for the two important cases of a thin planar source and a constant surface concentration are obtained in terms of the diffusivity of the fast streamD1(x). The expressions obtained for the trapping and releasing rates are found to be physically realizable. Expressions for the concentration of the diffusing substanceN(x, t) are obtained by considering suitable forms ofD1(x). By varying the parameters in the expressions for the functionN(x, t), concentration profiles are obtained which give a reasonable fit to the experimental data. A method is also developed to define the nominal Fick's diffusivity from the expressions of the apparent diffusivity. The values computed are of the same order‐of‐magnitude, but not in complete agreement, with those calculated using other methods.