The predicted structures and electronic properties of CeO(2) and Ce(2)O(3) have been studied using conventional and hybrid density functional theory. The lattice constant and bulk modulus for CeO(2) from local (LSDA) functionals are in good agreement with experiment, while the lattice parameter from a generalized gradient approximation (GGA) is too long. This situation is reversed for Ce(2)O(3), where the LSDA lattice constant is much too short, while the GGA result is in reasonable agreement with experiment. Significantly, the screened hybrid HSE functional gives excellent agreement with experimental lattice constants for both CeO(2) and Ce(2)O(3). All methods give insulating ground states for CeO(2) with gaps for the 4f band lying between 1.7 eV (LSDA) and 3.3 eV (HSE) and 6-8 eV for the conduction band. For Ce(2)O(3) the local and GGA functionals predict a semimetallic ground state with small (0-0.3 eV) band gap but weak ferromagnetic coupling between the Ce(+3) centers. By contrast, the HSE functional gives an insulating ground state with a band gap of 3.2 eV and antiferromagnetic coupling. Overall, the hybrid HSE functional gives a consistent picture of both the structural and electronic properties of CeO(2) and Ce(2)O(3) while treating the 4f band consistently in both oxides.