Ceria (CeO(2)) and india (In(2)O(3)) represent two of the most important metal oxide systems for catalytic and optoelectronic applications, respectively. Here, we report analytical interatomic potential models for these two materials, which reproduce the materials structural, elastic and dielectric properties. The potential models are then applied to study the fundamental defect reactions occurring in these materials. Further, we focus on the mechanisms of oxygen diffusion through the lattice, arising from anion Frenkel-pair formation, which is of particular interest for understanding the processes involved in radiation damage and catalysis. The thermodynamic barriers associated with the formation of the first stable anion Frenkel-pairs are 5.80 eV and 4.81 eV in cerium dioxide and indium sesquioxide, respectively; while for recombination, we calculate barriers of 0.78 eV and 0.23 eV. The threshold displacement energy for radiation damage in ceria is found to be 35.4 eV, in excellent agreement with recent experimental measurements, while for india we predict a value of 14.2 eV.