The classical two-film model for mass transfer between two fluid phases can only be used to describe the steady state mass transfer mechanism. Both the penetration and the film-penetration model are also valid solely when only one diffusion boundary layer exists at the interface between the phases. With a view to surmounting the limitations of the above models a new model has been developed for the mass transfer between two fluid phases with two diffusion boundary layers at the interface. The new model is based on the two-film concept and the Danckwerts distribution function, and is also able to simulate the unsteady state mass transfer mechanism between two fluid phases with two different boundary layers.