Marangoni convection plays an important role in hydrodynamics of liquid films on heated or cooled substrates. in this paper a model describing Marangoni convection, interface dynamics and evaporation in liquid films on composite substrates or substrates of functionally graded materials is developed. Non-uniform thermal conductivity of the substrate causes non-uniformity of temperature distribution at the liquid-gas interface which leads to appearance of Marangoni stresses, convective vortices and film deformation. The film dynamics is described in the framework of long-wave theory. The substrate thermal conductivity non-uniformity has a pronounced effect on transport processes in the liquid film. (C) 2009 Elsevier Ltd. All rights reserved.