Abstract: The invention relates to a device for the burr-free cutting of strip-shaped material, especially made of metal, which has, for each cut, two pairs of circular knives on axis-parallel knife shafts. The strip-shaped material is cut into by the first pair of circular knives in the first parting step and is severed in the opposite direction by the second pair of circular knives in the second parting step. The characteristic feature of the invention is that the counter-knives of the two pairs of circular knives are arranged on a common knife shaft so as to rest against one another, and that they consist of an outer rigid, especially metallic, cutting ring and of an inner annular elastomeric hub part.