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Using nanoparticles of CeO2 and ZrO2 prepared by chemical precipition method as the starting materials, the single-phase cubic Ce0.5Zr0.5O2 solid solution has been synthesized under high pressure and high temperature for the first time. The structural characteristics and valence state of the single-phase cubic Ce0.5Zr0.5O2 solid solution were investigated by XRD, TG-DTA, Raman, XPS and EPR measurements. The XRD results showed that the nanocrystalline mixtures of CeO2-50% ZrO2 can form a cubic Ce1-xZrxO2 solid solution above 1.67 GPa and above 1 073 Kt but the product is in a mixture state. The single-phase cubic Ce0.5Zr0.5O2 solid solution can be obtained only under the certain conditions of 3.1 GPa at 1 073 K. The high pressure promotes the process of the solid state reaction and the temperature of forming CeO2-ZrO2 solid solution decreases under high pressure. The DTA curve of the single-phase cubic Ce-0.5 Zr0.5O2 solid solution showed a broad exothermic peak between 403 K and 742 K. But the XRD pattern and Raman spectra displayed that the structure of the solid solution had not been changed before and after annealing at 773 K for 1 h. It revealed that the cubic Ce0.5Zr0.5O2 solid solution was stable in structure below 773 K. The EPR spectra recorded at room temperature gave an evidence of the presence of Ce3+ and O2- in CeO2 nanoparticles. However, the signals of Ce3+ and O2- have not been detected in Ce0.5Zr0.5O2 solid solution. An unknown signal (g = 1.990) has been observed in cubic Ce0.5Zr0.5O2 solid solution which has not been changed after annealing at 773 K for 1 h, exhibiting that there exists no Ce3+ in cubic Ce0.5Zr0.5O2 solid solution and the Ce4+ has not been reduced into Ce3+ after annealing. The hyperfine structure in Zr-3d XPS spectrum has been observed for the Ce0.5Zr0.5O2 solid solution. It shows that there may exist some Zr ions with a low valence-state. The ionic conductivity measured by impedance spectroscopy showed that the cubic Ce0.5Zr0.5O2 solid solution exhibits only the bulk conductivity. The bulk conductivity (sigma = 1.2 X 10(-5) S/cm at 823 K, sigma = 2.1 X 10(-3) S/cm at 1 123 K) is the same as that of CeO2, but smaller than that of Y2O3-stabilized ZrO2. A marked curvature at T = 823 K has been observed in the Arrhenius plot of the bulk conductivity. The activation energy below 823 K is lower than that above 823 K, and the reason has been discussed.