The products of andesite and dacite glaciovolcanism at Kerlingarfjöll are unlike others previously described in the literature. Three sequences of lithofacies are described and interpreted here. The andesitic deposits at "Campsite Gully" are divided into: massive vitriclastic lapilli tuff with intrusions; fluidal-clast-bearing vitriclastic lapilli tuff; and stratified, pumice-rich vitriclastic lapilli tuff. At Tindur, andesitic eruptions produced contorted pillow fragment breccia and the clast-supported lithic breccia. Finally, pillow lava with intrusions and crudely-bedded vitriclastic lapilli tuff of dacitic composition are described at Haraldur. Abundant vitriclasts, the presence of pillow lavas, hackly fracturing of lava bodies and lack of oxidation of clasts demonstrate that each of these lithofacies formed in the presence of abundant water. This contrasts with all other descriptions of subglacially-erupted intermediate magmas, which are characterised by jointed and glassy lava flows and domes with a marked scarcity of fragmental material. The Kerlingarfjöll sequences therefore demonstrate that it is possible for intermediate magmas to generate and interact with significant volumes of water at the base of a glacier. Preliminary estimates of volatile contents in glassy clasts correspond to quenching pressures equivalent to > 500 m water or > 550 m ice. This is consistent with eruption beneath an ice sheet that was thick enough to overwhelm the underlying topography and where meltwater drainage was controlled by the morphology of the glacier surface. It is argued that the drainage of water due to steep topography and/or thin and fractured ice, as opposed to thermodynamic considerations, is the most likely explanation for the absence of evidence for significant magma-water interaction in previously described instances of intermediate glaciovolcanism. The apparent low viscosity of the Kerlingarfjöll magmas may relate to relatively high eruption temperatures and/or the inhibition of degassing of the magma due to high ambient pressures and the consequent limitation of groundmass crystallisation.