Peralkaline rhyolites of the Greater Olkaria Volcanic Complex, Kenya Rift Valley, were derived from separated, though closely related, magma chambers. Ion microprobe analyses of glass inclusions in quartz phenocrysts show pre-eruptive water contents of up to 3.4 wt% contrasting with previous estimates that the magmas were anhydrous. The values approach predicted solubility levels corresponding to water saturation at low crustal pressures (1 kbar). The glass matrices of the rhyolites have low water contents, ranging from 0.07 to 0.46 wt%, suggesting significant degassing during, or prior to, eruption. Infrared measurements of the matrix glasses show variation in the relative proportions of the two hydrous species dissolved in the glasses. The amount of molecular water, determined semi-quantitatively, apparently increases with increased fluorine content and peralkalinity. This suggests a competition between hydroxyl groups and fluoride ions for similar sites within the melt structure. The mechanism of degassing has been investigated using hydrogen isotopes. The range of D values in most rocks can be produced by varied degrees of open-system degassing of rhyolite melt initially in equilibrium with water of a fixed, or limited, D value. There is evidence to suggest that closed-system degassing may also have been a significant component in some rhyolites. The exact mechanisms of degassing remain uncertain. Particular problems include the relative contribution of open-and closed-system degassing during eruption and the initial vapour compositions and solubility relationships.