Recent new mixing and combining rules for cubic equations of state (EOS) have extended the range of such equations to the accurate description of the vapor-liquid equilibria (VLE) of highly nonideal mixtures. However, the simultaneous correlation and/or prediction of vapor-liquid equilibrium (VLE) and liquid mixture excess enthalpies (H-ex) by either activity coefficient models or equations of state has been a difficult problem in applied thermodynamics. In this communication, we re-examine this problem using a modified version of the Peng-Robinson equation of state and the two-parameter van der Waals one-fluid, Wong-Sandler and modified Huron-Vidal mixing rules. For comparison, the direct use of activity coefficient models is also considered. In each case a temperature dependence of the model parameters is introduced in an attempt to represent simultaneously VLE and H-ex behavior. Four highly nonideal binary mixtures (2-propanol + water, methanol + benzene, benzene + cyclohexane, and acetone + water) are considered. The results indicate that while all the models can accurately correlate VLE and H-ex data separately, attempting to predict the values of one property with parameters obtained from the other does not give satisfactory results with any model. Also, we find that the simultaneous correlation of both VLE and H-ex with the EOS models at one temperature is possible, but extrapolations to other temperatures with parameters obtained in this way did not result in accurate predictions of either VLE or H-ex. The main problem appears to be that the excess free energy (activity coefficient) models used are not capable of representing both VLE and H-ex over a range of temperatures, and so equations of state that incorporate these free energy models have the same shortcoming.