Abstract: A rotary die cutter unit with rapid die connection has a die equipped with connecting bars, and a die-holding cylinder. The die-holding cylinder has longitudinal grooves with openings receiving the bars when connecting the die to the die-holding cylinder. Connecting teeth, which are housed in the openings of the grooves, circumferentially move on the cylinder, and assume a non-connected position in which they are completely moved out from the grooves, and a connected position in which they protrude into the grooves. Control elements corresponding to the grooves are provided, having small irregular teeth with one of the two sides whose height is progressively decreasing in the form of a chute. The control elements, when longitudinally moving, act on roller bearings to gradually move the connecting teeth between their two extreme connected and non-connected positions.