Abstract: To make blocks of bags having blocked stubs, which are joined by perforation lines substantially only to the lower opening-defining edge of each block, which lower edge is separated by a substantially continuous slit from the upper opening-defining edge, a tubular web of synthetic thermoplastic material is formed in partial regions with perforation lines extending through both plies. Only the upper ply is cut to form separating slits extending substantially throughout the width of that upper ply. The bags are then separated from the tubular web by hot-wire welding and are stacked.