<p>Apparatus for processing flat strip material including cutting apparatus for cutting the material and to strip portions and stacking apparatus having air cushion means for stacking the strip portions one on top of the other. An accelerating anchoring roller, having vacuum or magnet devices therein for attracting the sheet portions thereto are provided for the exclusive transfer of the strip portions from the position were cut in the cutting apparatus in positions at the inlet of the stacking apparatus where the air cushion takes over the conveyance and stacking of the strip portions.</p>