The Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state are probably the most widely used cubic equations of state in the refinery and gas-processing industries for the prediction of vapor-liquid equilibria for systems containing nonpolar components. The new mixing rules which have recently been developed that combine liquid activity models with the equations of state, however, have extended the application of such equations to highly nonideal systems. A new zero-pressure-based mixing rule is presented here that reproduces, with extremely high accuracy, the excess Gibbs free energy as well as the liquid activity coefficients of any activity model without requiring any additional binary interaction parameters. We examine the performance of the Peng-Robinson and Soave-Redlich-Kwong equations of state using the NRTL liquid activity model with binary parameters determined at low temperatures in this new mixing rule, MHV1, and Wong-Sandler for the prediction of high-pressure and high-temperature phase equilibria.