In the present work, we have used density functional theory (DFT) and DFT+U to investigate the crystal structure and phase stability of four model compounds in the Ln 2 O 3-UO 2-UO 3 ternary oxide system: La 2 UO 6 , Ce 2 UO 6 , LaUO 4 , CeUO 4 , due to the highly-correlated nature of the f-electrons in uranium. We have considered both hypothetical ordered compounds and compounds in which the cations randomly occupy atomic sites in a fluorite-like lattice. We determined that ordered compounds are stable and are energetically favored compared to disordered configurations, though the ordering tendencies are weak. To model and analyze the structures of these complex oxides, we have used supercells based on a layered atomic model. In the layer model, the supercell is composed of alternating planes of anions and cations. We have considered two different ordering motifs for the cations, namely single species (isoatomic) cation layers versus mixed species cation layers. Energy differences between various ordered cationic arrangements were found to be small. This may have implications regarding radiation stability, since cationic arrangements should be able to change under irradiation with little cost in energy.