A communication game system includes a plurality of game apparatuses which are able to wirelessly communicate with each other. Each of the game apparatus registers identifying information of an opponent obtained by a short-distance wireless communication or by user's input in a friend list. Thereafter, the game apparatus connects to the Internet, and inquires server, etc. whether or not it is possible to communicate with the opponent in the friend list over a network. If it is possible to communicate, the game apparatus obtains an address of the opponent to make a network communication. In a case that a still another opponent being connected to its own apparatus exists, when other game apparatus makes a connection, its own game apparatus transmits their identifying information to introduce the communicating opponents to each other. The game apparatuses introduced to each other make a communication over a network, and add the identifying information of the opponents to the friend list, if necessary.