A method of providing a service to a terminal device via the Internet from a service provision apparatus in response to access from the terminal device includes the steps of (a) establishing and maintaining connection between the service provision apparatus and a relay device specified by a global IP address on the Internet at a request for connection of the service provision apparatus so that the service provision apparatus and the relay device are in communication with each other via the Internet, (b) accessing the service provision apparatus for the service by way of the relay device from the terminal device connected thereto, and (c) providing the service from the service provision apparatus to the terminal device by way of the relay device.