The authors report Monte Carlo simulation results on cation ordering in a range of fluorite-related phases in various ZrO₂-LnO_1.5 systems. They restrict their attention to the face-centred cubic array of cations, assuming that the effect of the anion array upon the cation ordering can be simulated via effective cation-cation interactions. The basic interactions of the model include strongly repulsive nearest- (J₁) and next-nearest-neighbour (J₂) effective pair interactions and a three-spin interaction (J₃) term for the nearest neighbours. The ionic size difference between the two cation species is a measure of the strength of the interaction parameter J₂ and is a controlling factor for different kinds of ordering arrangement. While pyrochlore-type ordering is found to be stable for large values of J₂, the c-type phase is observed for small values of J₂. Both phases are found to coexist in the intermediate-parameter range. The authors report complete phase diagrams for two sets of interaction parameters computed within the framework of the 3D Ising model. The simulation results are consistent with electron and X-ray diffraction results on these mixed rare-earth oxide systems.