Double diffusive steady natural convection in a vertical stack of square enclosures, with heat and mass diffusive walls, is studied numerically; The main objectives of the paper are the statement of the complete mathematical model for this kind of problem, and the presentation and analysis of some significant results showing the influence of the heat and mass transfer participating walls. The analysis is concentrated on a restricted set of numerical results, obtained from a limited set of particular combinations of the governing dimensionless parameters for a cavity filled with moist air. The heat and mass transfer characteristics of the vertical stack are analysed through the heat and masslines, and the local and global Nusselt and Sherwood numbers over all the walls of the cavity.