To minimize the scales of a storage area and a processing area which constitute a management device by performing connection management in a device or a system, based on a connection number proper to the self-device or the system which is defined in accordance with a connection number that can be handled.

The parts of a VPI and a VCI which specify connection to which an ATM cell belongs are separated by a header separating part 1a of a converting part and are given to a conversion table 1b that, stores an identification number proper to a device and an attribute information which are used in the device in exchange for the VPI and VCI. In such a case, when a connection number that can be handled in the device is 4096, the identification number that is given by full 28-bits on a network are converted into a 12-bit identification number proper to the device. After that, the ATM cell is managed with the identification number proper to the device, is converted into the original identification number in the network again after undergoing various processing based on each identification number and is outputted from an output side.