The formation of tetragonal Zr0.5Ce0.5O2 Solid solution nanocrystallites of 5 +/- 1 nm size by a hydrothermal method at 120 degrees C for 6 h was confirmed by careful Raman and XRD studies for the first time. It was characterized as the C-form with an axial ratio of c/a = 1 but with oxygen ion displacements. The asprepared sample was hydrous in nature, which is responsible for the lattice expansion. However, most of the water held in the structure can be expelled by heating the sample above 600 degrees C. Above 1050 +/- 50 degrees C the C-form of tetragonal Zr0.5Ce0.5O2 solid solution dissociates into two phases, cubic phase and the t-form of tetragonal phases.