A data transmission-reception system is disclosed wherein, after the radio wave condition becomes good, backup processing is performed immediately without performing confirmation of the memory capacity of a portable radio terminal thereby to allow efficient transmission-reception of data such as an electronic mail. Information of a mail server is received by a portable telephone terminal through a dialup server and then transferred to an electronic mail terminal. In this instance, when the radio wave condition is good, a card loaded in the portable telephone terminal accesses the mail server as a representative of the electronic mail server and fetches electronic mails stored in the mail server and destined for the user into the electronic mail terminal through the dialup server and the portable telephone terminal. Here, the fact that the radio wave condition exhibits that reception of the radio wave is possible is used as a trigger to perform reception of transfer data without performing discrimination of whether the transfer data can be stored into a memory of the portable telephone terminal. Then, the transfer data are not stored into the portable telephone terminal but stored directly into a memory of the electronic mail terminal.