Abstract: A system for interconneting local networks via a public transmission network, in which equipment items of the microcomputer type, connected to a local network A, are capable of being connected to the public network by a router X in order to communicate with one or more equipment items of the microcomputer type connected to at least one other local network B, which are capable of being linked to the public network by a router Y.The system includes security protection of the establishment of the communications between the local networks over the public network, implementing a certificate exchange mechanism and the software procedures for active authentication, of the "challenge-response" type being placed in the routers.