The thermodynamical stability boundaries for the Xe hydrate system were investigated in a pressure range up to 70 MPa and a temperature range from 290 to 320 K. In the critical temperature series of the guest molecules, the Xe hydrate is identified to be the border hydrate system having no quadruple point of(hydrate+two liquids+gas). The three-phase coexisting curve of (hydrate+liquid Xe+gas) terminates at the critical end point (289.76 K, 5.86 MPa) of (hydrate+liquid=gas) very close to the critical point of pure Xe fluid. The three-phase coexisting curve of (hydrate+water+gas) exhibits the characteristic 'S-shape' as if there would exist the quadruple point. The enthalpy change of Xe hydration was also evaluated from the Clausius-Clapeyron equation; the average value of 65 kJ/mol is almost constant in the whole temperature range along with the three-phase coexisting curve.