The present paper reports the phase progression in nano-crystalline oxides PrO₂ and CeO₂up to pressuresof 49 GPa and 35 GPa, respectively, investigated via in situ Raman spectroscopy at room temperature.The samples were characterized at ambient conditions using X-ray diffraction (XRD), AFM, and Ramanspectroscopy and were found to be cubic with fluorite structure. With an increase in applied pressurethe cubic bands were seen to steadily shift to higher wavenumbers for both the samples. However,we observed the appearance of a number of new peaks around a pressure of about 34.7 GPa in CeO₂and 33 GPa in PrO₂ which were characteristic of an orthorhombic  α-PbCl₂ type structure. The mode Gruneisen parameters for both the phases were obtained from the pressure dependence of frequencyshifts. On decompression, the high pressure phase existed down to a total release of pressure.