The oxygen nonstoichiometry (x) of UO$_{2+x}$ and $(Ce_yU_{1-y})O_{2+x}$ (y=0.05, 0.25) has been measured as a function of oxygen activity (a02) at 100$0^{circ}C$ by a solid state coulometri titration technique. The results for UO$_{2+x}$ are in a good agreement with literature data and the ao2-dependence of the nonstoichimetry has been well explained with (2:2:2) cluster model. The equilibrium oxygen activity of $(Ce_yU_{1-y})O_{2+x}$ increases with Ce-content (y) for given nonstoichiometry (x), which is ascribed to the fact that Ce is present as Ce$^{3+}; and; Ce^{4+}$, and, therefore, the addition of Ce reduces the oxidation capacity of UO$_{2+x}$. From the oxygen activity dependence of x in $(Ce_yU_{1-y})O_{2+x}$ the defect structure of $(Ce_yU_{1-y})O_{2+x}$ is discussed.