Structural reappraisal of several classic rheomorphic ignimbrites in Colorado, Idaho, the Canary Islands and Italy has, for the first time, revealed abundant oblique folds, curvilinear folds and sheathfolds which formed during emplacement. Like their equivalents in tectonic shear-zones, the sheathfold axes lie sub-parallel to a pervasive elongation lineation, and appear as eye structures on rock surfaces normal to the transport direction. With the recognition of sheathfolds, ignimbrites previously inferred to have undergone complex rheomorphic deformation histories are re-interpreted as recording a single, progressive deformation event. In some examples, the trends of sheathfolds and related lineations change with height through a single ignimbrite suggesting that rheomorphism did not affect the entire thickness of ignimbrite synchronously. Instead, we infer that in these ignimbrites a thin ductile shear-zone rose gradually through the aggrading agglutinating mass whilst the flow direction varied with time. This suggests that, in some cases, both welding and rheomorphism can be extremely rapid, with ductile strain rates significantly exceeding rates of ignimbrite aggradation. ?? Springer-Verlag 2004.