The AGAPE model was introduced in the first paper of this series. The model allows the calculation of phase equilibria from a consideration of whole, rather than segments of, molecules and requires two general physical parameters which can be obtained from two parallel procedures. The first parameter is entropic while the second is energetic. In this paper, the model is applied to the subject area of liquid-liquid equilibria (LLE) and all the necessary equations are derived. A third procedure (LLE-fit) for obtaining the two parameters is given here. This uses the critical solution temperature which for a number of binary mixtures are predicted using the earlier generalised London potential (GLP) and the vapour-liquid equilibria (VLE)-fit procedures. All three procedures are then used to predict the temperature-composition (T-x) profiles for a number of mixtures. The results show that the fit procedures produced good results and generally performed better than the GLP due, primarily, to the type of compounds involved in LLE. The VLE-fit procedure performs as well as the LLE-fit procedure, indicating the generality of the model.