This study demonstrates that SAFT EOS models might exhibit the practically unrealistic and even non-physical predictions due to the two factors, namely the temperature dependencies of a segment packing fraction and the very high-polynomial orders by volume. The first factor is responsible for predicting the negative values of the heat capacities at very high pressures and the intersections of isotherms at high densities. The very high-polynomial orders of several SAFT EOS models result in prediction of the additional stable unrealistic critical points and the pertinent fictive phase equilibria. It is demonstrated that the unrealistic phase splits might present the globally stable states established by the models, while the VLE matching the experimental data might be in fact metastable. In addition, the excessive complexity of certain SAFT models might result in wrong prediction of auxiliary thermodynamic properties of the experimentally available fluid phases. The undesired predictions discussed in the present study arise queries regarding the robustness and the over-all physical validity of the models under consideration in their present forms. This study discusses the ways of removing the numerical pitfalls. (C) 2010 Elsevier B.V. All rights reserved.