An arbitrarily positioned lateral perforation forming apparatus can form a lateral perforation at an arbitrary position or selected position in a continuous web paper at high precision by a simple
control system with small control amount. A lateral roulette cylinder projecting a lateral roulette edge on its outer periphery, arranged on one side of the continuous web paper and rotating in a traveling direction of the continuous web paper; and a receptacle cylinder projecting an edge projecting portion opposing to the lateral roulette edge of the lateral roulette cylinder on its outer periphery, arranged on the other side of the continuous web paper, rotating in the traveling direction of the continuous web paper, and forming a lateral perforation in the continuous web paper when the edge receptacle portion opposes the roulette edge; are rotated in
synchronism with traveling of the continuous web paper in the drive
system. Furthermore, the arbitrarily positioned lateral-perforation forming apparatus includes a first differential mechanism disposed in an element connected to one of the lateral roulette cylinder and the receptacle cylinder in the drive
system, causing difference in rotational phases of the lateral roulette cylinder and the receptacle cylinder by varying rotation of a differential shaft thereof for selectively placing the edge receptacle portion at a position opposing to the roulette edge and a position circumferentially offsetting from the roulette edge, and a first
control unit for controlling rotation of the differential shaft of the first differential mechanism.