Isotherms have been obtained for the adsorption of water from a number of electrolyte solutions (0$\cdot$7 molal to near saturation) on montmorillonite and illite. The interlamellar volumes of the montmorillonite at various points on the isotherms have been calculated from X-ray diffraction results. For some systems isotherms have been measured at three temperatures. Attempts to account for the shapes of the isotherms by means of a simple Donnan equilibrium causing exclusion of ions from the surface region were not successful. The exclusion of electrolyte was always much greater than predicted by the Donnan theory. The isotherms usually show three discontinuities with increasing electrolyte concentration, corresponding to the inability of electrolyte to penetrate into three surface regions until particular concentrations have been exceeded. One of these regions (which is never penetrated by electrolyte molecules, even at concentrations near saturation) corresponds to the primary hydration shell of the exchangeable cations. Entry of electrolyte into the other regions is governed by the image force between the ions and the surface region and hence the difference between the dielectric constant of the bulk and surface water. When these approach equality, entry is controlled by the need for electrolyte ions to undergo suitable ion pairing and to decrease the entropy of an already ordered surface rendering it more like the electrolyte solution. The ability of an electrolyte to enter the surface regions is correlated with the balance between the relative structure making and breaking power of an ion. The free energy of penetration of an electrolyte into the adsorbed water increases with decreasing hydration. Thus adsorption of water on illite from caesium chloride solutions does not occur over the concentration range used. The similarity of the results obtained for illite with predominantly external surfaces, and montmorillonite with predominantly internal surfaces, is of special significance. It indicates that the adsorption of two layers of water provides the bulk of the energy for intercrystalline swelling which is common to all clays.