The nonrandom mixing version of the Holey Huggins theory for pure components presented in a previous paper is extended to binary mixtures and is applied to the miscibility behavior of the systems polystyrene/methyl acetate and polystyrene/cyclohexane. Comparison with the experimental data shows that the present theory is successful in predicting the miscibility behavior and its pressure dependence for these two systems. For polystyrene/cyclohexane the results of the random mixing and nonrandom mixing theory are comparable. For this system one indeed does not expect that nonrandomness will be very important. For the system polystyrene/methyl acetate the agreement between theory and experiment improves by applying the nonrandom mixing theory, indicating that nonrandom effects are of importance.