To conduct communication at a high speed and efficiently, when performing data communication among various terminals.

Before starting the communication between terminals, a data-transmitting terminal acquires information about extension capability in a data-receiving terminal and the network speed of a network 40, by performing preliminary communication between the data transmitting terminal and the data-receiving terminal, selects a compression system and compression rate, in which effective transfer speed becomes maximum, compresses the data after informing the receiving terminal of the compression system and the compression rate and starts transfer of the compressed data. In the data-receiving terminal, the received compressed data are extended by an extension system, corresponding to the informed compression system. The extension capability in the data-receiving terminal is determined, based on processing speed of a CPU which the data-receiving terminal possesses.