The minimisation of the distance function between the Gibbs energy of mixing and its common tangent plane (or line) is applied to adsorbed solutions. A specific algorithm to deal with the associated bilevel programming problem is presented and discussed. This approach is validated with experimental data and ideal adsorbed solution theory calculations for an ideal case and with experimental data for two nonideal cases at low and high pressure. While the presently adopted non-ideal formulation provides solutions fulfilling only the necessary condition for equilibrium, the common tangent plane approach proposed in this paper enables the direct evaluation of the necessary and sufficient solution. (C) 2015 Elsevier B.V. All rights reserved.