Abstract The roughness of the surface resulting from a multiple-layer adsorption is treated as a function of the temperature and the supersaturation. It is shown that the supersaturation Δμ (i) v7, at which the number of vacancies and admolecules of the i-th top-layer are equal, is the arithmetic mean of the equilibrium supersaturations Δμ (i) 0 and Δμ ( i + 1) 0 of the i-th and ( i + 1)-th layers respectively, contrary to a three-dimensional phase, where Δμ v7 and Δμ 0 are identical (nil). The further use of Δμ (i) v7, as origin for the supersaturation scale, leads to reduced equations, permitting to calculate easily roughness and surface free energy variations in the stability range (Δμ (i) 0 < Δμ < Δμ ( i + 1) 0) of the i-th layer. The total free surface energy variation due to multiple layer adsorption is decomposed into two parts: the first, due to the deposition of i compact layers, and the second, due to the roughness of the top monomolecular layer. A method is proposed for determining the absolute specific adhesion energy between two substances (A and B) in the case when only the positions of the steps of the experimental step-wise isotherm of A on B are known. The method is applied to the adhesion energy xenon/graphite.