Welded tuffs formed by air fall, rather than by pyroclastic flow, are a common type of volcanic rock. Examples of welded air-fall tuffs are the Thera and Therasia welded tuffs, Santorini volcano, Greece, and parts of the ejecta of the 1875 eruption of Askja, Iceland. The Thera and Askja welded tuffs cover a few square kilometres, and the Therasia welded tuff covers at least 6 km 2 . The Santorini tuffs and parts of the Askja deposit grade laterally and vertically into nonwelded, coarse-grained Plinian air-fall pumice deposits. The nonwelded equivalents of the welded tuffs have grain-size characteristics and depositional features typical of airborne ejecta, such as good sorting (σ < 2.0), internal stratification, distinguishable fall units, and a systematic decrease in thickness and maximum and median grain size away from the source. Zones of dense welding, partial welding, and no welding are similar to zones in ignimbrites. A zone of marked color change was also observed in the nonwelded part. Lateral zonation is well developed. The tuffs are most densely welded where the thickness is the greatest. Zone boundaries are parallel to isopachs for the uncompacted thickness. In the zone of dense welding of the Askja tuff, the tuff is welded from bottom to top, although no significant overburden has been removed since 1875. Vertical profiles of strain ratio, porosity, and density were determined for the thickest parts of the three tuffs. There are systematic increases in strain ratio and density and decrease in porosity toward the central parts of the welded zone in the Santorini tuffs and the lower central part of the Askja tuff. The Askja and Thera tuffs show notable fluctuations of strain ratio, porosity, and density superimposed on the general compaction profile. These fluctuations are attributed to the heterogeneous nature of the stratified air-fall ejecta and may be one way of distinguishing tuffs of air-fall and pyroclastic flow origins. Two air-fall units were traced laterally from the zone of dense welding to the zone of partial welding. The strain ratio of the clasts and the porosity and density of tuff change in a rapid linear manner over a distance of only 70 m. Marked lateral changes in strain and welding, normal to isopach contours, are considered evidence that rapid accumulation is critical in producing welding in air-borne ejecta. Historical records indicate that the Askja tuff was erupted in less than 1 h. An accumulation rate of 20 cm/min is estimated for the area of densest welding, before compaction occurred. All three of the welded tuffs show evidence of physical mixing of contrasted magma compositions: the Askja tuff contains rhyolitic and basaltic components, and both Santorini tuffs contain dacitic and andesitic components. In all three, the volume of the mafic component is minor, and superheating of the silicic component probably contributed to produce welding.