We report molecular simulation studies of liquid-liquid equilibria (LLE) in mixtures that include polar (water/methanol) and nonpolar/weakly polar (cyclic) components. While vapor-liquid equilibria (VLE) has been widely studied using molecular simulations, there have been relatively few such studies for LLE despite their industrial importance. Often equation of state parameters that work for VLE do not work well for LLE, our studies show, however, that molecular potentials for VLE were successful in predicting reliable results for LLE. Our methodology is an extension of our previous studies for VLE (solubility of gases in liquids). In these studies, we used the generalized AMBER force field (GAFF) with no further adjustments. Our results showed good agreement with recent experimental results for LLE of these systems and showed some interesting trends. We found that the behavior of mixtures of hydrocarbons with both methanol and water present became significantly different when no water was present. After validating our method and models in our LLE studies, we also used these simulations to explore other dynamic and equilibrium properties of these mixtures. Our results showed significant changes in the structural and dynamic behavior of these mixtures as the concentration of water changed. (C) 2017 Elsevier B.V. All rights reserved.