X-ray diffraction experiments under high pressure have been carried out for ZrS₂ and PbI₂ with the CdI₂ structure. With increasing pressure, the z-value of ZrS₂ increases monotomcally from 1/4 at 1 bar to 0. 27 at 8 GPa, and the phase transition to a high-pressure phase takes place gradually around 10 GPa. On the other hand, PbI₂ with the larger z-value of 0. 265 at ambient conditions undergoes the phase transition to a high pressure phase at a lower pressure of 0. 9 GPa. The crystal structure of the high pressure phase, however, has not been determined yet.