A plurality of private address spaces where private addresses may possibly overlap are connected with a global address space. Respective private address spaces possess VLAN-IDs as identification information for VLANs. When connecting the respective private address spaces with the Internet, a duplicate network address translating device performs, with VLAN-ID and the private address of the respective private address spaces in pairs, mutual translation between the private address and global address of the Internet. A duplicate addresses-handling server is provided with a routing table which shows the relationship between virtual interfaces corresponding to VLAN-IDs and addresses of the respective private address spaces. A server portion of the duplicate addresses-handling server records, if a request is made from apparatuses of a private address space, the request and VLAN-ID, refers to, if making a response thereto, the routing table, selects a virtual interface which corresponds to the address of the response receiver, and makes a response. A virtual interface processing portion gives an applicable VLAN-ID and carries out an output to a switching hub.