In this paper, we have tested how accurately our improved form of perturbation theory and van der Waals one-fluid theory can predict recent simulation results for vapor/liquid, liquid/liquid and gas/gas equilibria of highly nonideal binary mixtures. In these mixtures, size and energy parameters of the like as well as unlike components differ significantly. Comparisons of theoretical predictions with simulation results for vapor/liquid and liquid/liquid equilibria show a very good performance of perturbation theory in different nonideal conditions. Prediction of gas/gas equilibria of mixtures with large unlike size parameter is only qualitative. Van der Waals one-fluid theory is successful in predicting vapor/liquid equilibria of moderately nonideal mixtures only. It becomes less reliable in describing liquid/liquid and gas/gas equilibria of highly nonideal mixtures.