A tearing-off roller pair, for tearing off sections or strips divided by perforation cuts from a material web, consists of a first roller with a substantially smooth steel shell and, applied against it, a second roller with a resilient body set into it for increasing the contact pressure, which resilient body projects above its peripheral surface in its unstressed state. To allow a greater retaining force to be exerted on the sections to be torn off, several of the resilient bodies are set in a recess along a cylindrical surface of the second roller.