We have carried out high-pressure X-ray structural studies of BeO and ZnO up to 200 GPa to find the phase transition of BeO from the wurzite to the NaCl structure and that of ZnO from the NaCl to the CsCl structure, which are expected theoretically. The phase transition of BeO occurred at 137 GPa, which is in good agreement with the theoretical value of 139 GPa. The wurzite phase persisted up to 175 GPa. The bulk modulus of BeO at zero pressure is determined to be 223 GPa by the Birch's equation. As previously reported, the ZnO sample transformed from the wurzite structure to the NaCl structure at 9.1 GPa. Extending the pressure range up to 202 GPa no phase transition to the CsCl structure occurred. The bulk modulus of the NaCl structure was determined to be 194 GPa.