Mixed actinide oxides (MOX) have been used as nuclear fuel material, furthermore UO2 fuel effectively becomes a mixed oxide during reactor operation due to transmutation and decay. As a result, understanding the behaviour of MOX is of considerable importance. In particular, the phase diagram of these MOX systems is an important tool as it defines the operational limits for nuclear fuel. Molecular dynamics (MD) is a useful tool used to predict the melting points of these system. However, these systems can be solid, a mixture of solid and liquid or liquid and predicting the solidus and liquidus lines can be challenging. A new method has been developed to predict points on these solidus and liquidus lines using MD simulations. Calculations are carried out on (U,Pu)O2, (U,Th)O2 and (Th,Pu)O2 MOX systems and compared to experimental data. These simulations can help to provide important insight into how these systems behave at high temperatures.