A new equation of state for associating fluids has recently been presented by Medeiros and Tellez-Arredondo, the Cubic-Two-State Equation of State (CT'S EoS) [Ind. Eng. Chem. Res. 47 (2008) 5723]. This equation arises from the coupling of the Soave-Redlich-Kwong EoS (SRK) with an association term from a two-state association model. The CTS EoS is polynomial in volume and it is able to describe vapor pressures and molar volume of associating fluids such as water, alcohol and phenol, among others. The equation is also able to describe the liquid-vapor equilibria of their mixtures with alkanes. In this paper, the physical and thermodynamic foundations of the CTS EoS are further investigated. In order to verify its applicability for cross-associating systems, the equation was employed in the prediction of phase equilibria behavior of binary alcohol-alcohol and water-alcohol mixtures. Very good agreement between predictions and experimental phase equilibria data was obtained with very simple combining rules and only one adjustable binary parameter. No additional parameters were necessary to describe ternary systems. With the purpose of checking the model's hypothesis and limitations, the two-state association term was coupled with the hard sphere Carnahan-Starling EoS, forming the CS-TS equation and the association characteristic parameters were determined theoretically for prototype association fluids. Monte Carlo NPT simulations of such fluids were performed and the results were compared with the equation's predictions. The CS-TS was able to describe qualitatively the pvT behavior of the prototype; nevertheless, it is not as accurate as those predictions obtained from the combination CS with Wertheim's association term. It seems that, when adjusting parameters of the CTS EoS to real substances, the discrepancies between the predicted and the real association contribution are dissipated among other adjustable parameters, specially on the dispersive term of the SRK equation. Finally, it is shown that CTS EoS isotherms can only have one or three real bigger roots than the co-volume for positive pressures, similar to cubic equations of state, and then it has the desirable form to describe vapor-liquid phase equilibria of associating compounds mixtures. (C) 2010 Elsevier B.V. All rights reserved.