The densification and grain growth mechanisms of $UO_{2+x}$ in $H_2$ and in $CO_2$ have been investigated. Uranium dioxide powder compacts were sintered at 1$700^{circ}C$ in $H_2$ or at 110$0^{circ}C$ in $CO_2$ for various times from 0.5 h to 16 h. The grain size and density of the specimens were measured. From the measured data, the mechanisms of the densification and grain growth were determined by use of available kinetic equations which express the relations between densification and grain growth. In both atmospheres, it has been found that the densification was controlled by the lattice diffusion and the grain growth by the surface diffusion of atoms around pores. It appears that the surface diffusivity as well as the lattice diffusivity increase considerably with the increase in O/U ratio in the specimen.