Microstructures of ZrO//2-CeO//2 ceramics were investigated with arc-melted specimens by means of TEM, TEM-EDX, ED and XRD. (1) As-cst specimens with more than 15 mol percent CeO//2 consisted of a relatively stable cubic phase having super sub-lattice of O**2** minus ions. The reciprocal lattice was obtained. (2) By annealing the cubic phase in air, the superstructure disappeared, and the transition from cubic to tetragonal phases easily took place. (3) During prolonged annealing a nucleation-growth type coherent precipitation took place. (4) Phase boundaries of the cubic and tetragonal phases in the diagram of the ZrO//2-CeO//2 system were determined. (5) Sintered 12 mol percent CeO//2 transformed easily into a monoclinic phase by pulverizing.