Peralkaline welded tuffs from the islands of Gran Canaria, Canary Islands, and Pantelleria, Italy, show abundant evidence for post-depositional flow. It is demonstrated that rheomorphism, or secondary mass flowage, can occur in welded tuffs of ignimbrite and air-fall origin. The presence of a linear fabric is taken as the diagnostic criterion for the recognition of the process. Deposition on a slope is an essential condition for the development of rheomorphism after compaction and welding. Internal structures produced during rheomorphic flow can be studied by the methods of structural geology and show similar dispositions to comparable features in sedimentary slump sheets. It is shown that secondary flowage can occur in welded tuffs emplaced on gentle slopes, provided that the apparent viscosity of the magma is sufficiently low. Compositional factors favor the development of rheomorphism in densely welded tuffs of peralkaline type.