Semiempirical Interacting Bonds Method (IBM) in the slab approximation with due regard to relaxation after the free surface formation was used to calculate the surface energies and enthalpies of oxygen adsorption on the surface of ceria-based solid solutions. The IBM-estimated surface energies agree well with the published values obtained using electrostatic models or the periodic ab initio Hartree-Fock code CRYSTAL. The most weakly bound forms of the surface oxygen appear to be located at the (111) face on the cerium cations which have complex defects of non-stoichiometry in the subsurface layer.