The cubic-two-state (CTS) equation of state (EoS) was employed for modeling the liquid-liquid and vapor-liquid equilibria of nitriles + hydrocarbons (alkanes and aromatics) or water mixtures. For nitriles, the five pure compound parameters were determined by fitting the model simultaneously to experimental saturation pressure, density of saturated liquid, enthalpy of vaporization and liquid-liquid equilibrium data when mixed with n-dodecane. For alkanes, the pure parameters were those determined from conventional corresponding states correlations for Soave-Redlich-Kwong EoS. The van der Waals mixing and combining rules were applied for dispersive parameter and covolume, with a temperature-dependent binary parameter. In the case of nitrile mixtures with aromatics and water, cross-association were considered with the previously published CTS combining rules, and no association binary parameters were required. The correlations were very good in all cases. The model was also able to predict selective extraction of sulfur compounds (benzothyophene and benzothyophene 1,1-oxide) from alkanes. Because of its simplicity, therefore, the CTS EoS is a very attractive option for process simulation involving this class of mixtures.