The purpose of the present invention is to provide an Internet connection system which is capable of benefiting from the IPv6 by relatively easy manner and in which manufacturers of client-side devices can create added values for users. IPv6 packets are transmitted by a tunneling connection between a home network and a server on the Internet. Also terminal devices present in the home network can be uniquely recognized and controlled from outside via the server. Since all communications are performed via the server on the Internet regardless of the carrier and the ISP, the terminal device and all connections to the terminal device can be freely configured and controlled by the owner or the manufacturer of the server on the Internet.