A method and system for timely transferring electronic mail message over a communication network such as the Internet to a communication terminal to be transferred in accordance with a transfer trigger condition attached to the electronic mail message in advance, the trigger condition being specified by event information such as the movement and the operation of household appliance, living facility or positional information of specific terminal unit or other signals detected on the communication network. According to the present method, an electronic mail message is first sent to a communication server apparatus equipped on a communication network together with the transfer trigger condition, and after registering of the mail message, the communication server apparatus watches the transfer trigger condition and transfers the corresponding mail message of which transfer trigger condition meets a predetermined condition to a communication terminal unit to be transferred when the transfer trigger condition meets the predetermined condition.