The types of critical phase diagrams for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on a two-dimensional lattice gas theory are investigated. The search for critical point conditions was done using the Hicks and Young algorithm, switching to the Heidemann and Khalil algorithm in the close of vicinity of a critical point. We observed that the model can predict critical points that represent the conditions in which a vapor-like and a liquid-like adsorbed phases collapse. The critical diagrams were classified using an analogy with the van Konynenburg and Scott scheme for classifying the critical behavior of binary bulk mixtures. The original classification scheme is based on the critical lines on the pressure-temperature plane; we used a straightforward extension based on the critical lines on the spreading pressure-temperature plane. Five of the six types of phase behavior classified by von Konynenburg and Scott were observed using this thermodynamic model. The transitions between the types of phase diagram were also observed in temperature-mole fraction projections. These results extend previous observations that suggested the possibility of very interesting phase behaviors for adsorbed mixtures. However, experimental data would be necessary to confirm the predicted types of critical diagrams. (c) 2006 Elsevier B.V. All rights reserved.