An apparatus for overlapping and stacking sheets, the apparatus has a housing defining a stacking area and a travel plane for the sheets, a conveyor for transporting the sheets through the housing in a travel direction along a travel plane, and an overlapping device in the housing upstream of the stacking area for producing an overlapping stream of the conveyed sheets. A brake in the overlapping device slows the conveyed sheets of the overlapping stream. Stacking elements include stops projecting upward in the stacking area and serving to position a stack formed by the conveyed sheets of the overlapping stream. A separate frame carrying the stacking elements in the stacking area above the travel plane or extending to above the supply travel plane is mounted in the housing of the apparatus so as to be movable horizontally downstream in the direction away from the overlapping device.