Mathematical modeling of the convective processes caused by impact of various factors on the fluid media, such as shear flows and additional tangential stresses, gravity and thermocapillary forces and some other factors is rather important nowadays. The convective flows are often accompanied by interfacial mass transfer due to evaporation, The conditions to be applied at the interface between two interacting gas and liquid phases (the generalized kinematic, dynamic and energetic interface conditions) result from the strong discontinuity relations for mass, momentum and energy at interface. In the present paper construction of a mathematical model of flows of the evaporating liquid films on an inclined substrate is carried out. Mathematical modeling is based on the long wave approach of the Navier-Stokes equations coupled with heat transfer equation and of the generalized interface conditions. The exact solutions of the systems of equations for the zeroth and first orders of approximations with respect to a small parameter of the problem, are constructed in the two-dimensional case. An equation of the thin liquid films is derived for the case of the moderate Reynolds numbers. The equation incorporates the effects of gravity, viscosity, capillarity and thermocapillarity, co-current gas flow and evaporation.