Heat capacities of (U0.91Nd0.09)O-2, (U0.91Mg0.09)O-2 and (U0.85Mg0.15)O-2 were measured by direct heating pulse calorimetry over the temperature range from 300 to 1500 K. An anomalous increase in the heat capacity curve of these samples was observed above 1250, 1300 and 750 K, respectively, similar to those observed earlier in the cases of (U(1-y)M(y))O-2 (where M = Gd, La, Sc, Eu and Y) by the present authors. Assuming the anomalous increase is due to the formation of Frenkel defects of oxygen, the enthalpy of defect formation was calculated from the excess heat capacity. However, no anomaly was seen in the electrical conductivity curve of these samples around the onset temperatures of the anomalous increase in the heat capacity curve, suggesting that the anomalous increase is not due to the formation of electron-hole pairs. The difference in the onset temperatures of UO2 doped with various cations such as rare-earth elements and Mg was discussed in relation to the mean cation-oxygen interatomic distances which reflect the variety of the distribution of oxygens around the cations in the lattice, i.e. that of local structural environments for cation-oxygen bonding, The mean cation-oxygen interatomic distances were calculated from the ionic radii and the experimental lattice constants, assuming a perfect fluorite structure for these oxides. A linear relationship was found to exist between the onset temperature of the heat capacity anomaly and the difference in the mean cation-oxygen interatomic distance. The variety of local structures and defect clusters composed of Mg2+ and U5+ ions in UO2 are thought to be related to the heat capacity anomaly.