Abstract: A method and unit for transversely cutting cigarette portions or similar on a filter assembly machine, whereby a cigarette portion is fed transversely through a cutting station to intercept a rotary circular blade, which is maintained in a work position by an arm mounted to oscillate about an axis parallel to the axis of rotation of the circular blade, so as to move the circular blade between the work position, a store for worn circular blades, and a store for new circular blades.