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In this book, two-layer film flows down a vertical wall are studied. The integral method is used to derive an approximate system of evolution equations modelling long-wave flows of the film. Then, families of nonlinear steady-travelling periodic waves are computed. Computed waves have qualitatively similar behaviour to those found in one-layer films but the quantitative characteristics of the waves strongly depend on additional similarity parameters in the two-layer films. In particular, the average location of the interface between the layers affects the bifurcation scheme of the waves. To select the wave regimes which can be used to compare with experiments, systematic transient computations have been carried out to create a map of the attracting wave regimes, so-called dominating waves. For dominating wave regimes, the mass transfer problem for a weakly soluble gas is solved. In particularly, the absorption problem is systematically studied.