Abstract <p>The paper is devoted to a theoretical analysis of the nonlinear two-dimensional waves using the Navier–Stokes equations in their full statement. Varying the liquid Reynolds number, the Kapitza number and the wavy regimes wavelength, we consider the wavy liquid film flow both under and above the inclined plane in wide range of the inclination angle. We computed the steady-state traveling waves and carried out an analysis of their linear stability with respect to the disturbances with the same wavelength as the wavelength of the nonlinear solution. Previosly, the stability analysis of the nonlinear waves was carried out only for the case of the flow down a vertical plate. We obtained that the array of the bifurcations lines on plane of two parameters (the Reynolds number, the wavelength) depends essentially on the Kapitza number. The array dependence on the inclinations angle takes place only for the case of the flow under plate at large values of the inclination angle. We obtained dependences of the waves basic characteristics on the problem parameters and presented the typical film thickness profiles. We obtained also parameters where the negative <i>u</i>-velocity appears and where the waves have the closed contour lines of the streamline function. Iinstead of the traveling wave, the liquid drop falls down an inclined plane at these parameters.</p>