Mass-transport complexes (MTCs) form a significant component of many deep marine clastic successions. Here, studies of outcrop examples of MTCs from the Italian Apennines indicate that material can be entrained across both the upper and lower boundaries of a mass flow. The studied MTCs all incorporate debrite–turbidite couplets. Growth stratal geometries in the overlying turbidite sandstones indicate that turbidite deposition occurred synchronously with internal deformation within substrate debris flows. The turbidite stratal patterns and the internal structure of the debrites jointly indicate that at least the later stages of MTC emplacement were ordered, involving coherent creep. This process can generate unexpected sand-on-sand juxtapositions across otherwise low-permeability debritic horizons. Entrainment of substrate material across the lower debris-flow boundary occurred by thrusting, although this deformation can have initiated before the arrival of the further-travelled debris flow itself. The outcrop examples are thus characterized by composite deformation and depositional histories, such that different parts of composite MTCs can have experienced radically different amounts of displacement. The ordered creeping deformation recognized at outcrop may, however, be under-recognized in seismic examples, where internal deformation and associated growth stratal geometries are less easy to study.