Molecular simulation results using the exponential-6 intermolecular potential are reported for the phase behaviour of the atomic binary mixtures of neon + xenon, helium + neon, helium + argon and helium + xenon. These binary mixtures exhibit both vapour-liquid and liquid-liquid phase equilibria up to very high pressures. Comparison with experiment indicates good overall agreement. The results indicate that the exponential-6 intermolecular potential is a useful generic potential for molecular simulation.