von Stackelberg & Muller (1951) and Muller & von Stackelberg (1952) have shown that two structural types of water lattice exist in which various species are intercalated to give solid hydrates. In the present paper a statistical thermodynamic interpretation is given of the properties of these clathrate phases of water. This method is a development of a procedure applied by van der Waals (1956) to clathrate compounds of quinol, and shows that these hydrates should be non-stoicheiometric. It is possible to give a satisfactory explanation of the stabilizing action of 'hilfsgase' (von Stackelberg & Meinhold 1954); to interpret various thermochemical quantities and indicate limitations in some of these quantities as previously determined; and to clarify the conditions under which the clathrate phases form. Calculations of heats of intercalation for several inert gases give values close to those derived from thermochemical data. Calculations of equilibrium constants for intercalation of these inert gases lead to reasonable estimates of dissociation pressures of the corresponding clathrates. On the basis of the dissociation pressures the fractionation of mixtures to be expected by formation of clathrate phases may be estimated.