A game system includes plural game apparatuses, and the respective game apparatuses are communicably connected to one another. For example, when a communication game is interrupted, a player closes his/her own game apparatus. In such a case, prior to setting of a sleep mode, the game apparatus notifies all other game apparatuses of the interruption of the communication game, and then the game apparatus saves parameters necessary to execute a game main processing program to interrupt the execution of the game main processing program. When the other game apparatuses receive the notification on the interruption of the communication game, the other game apparatuses save the parameters to interrupt the execution of the game main processing program. In resuming the communication game, the respective game apparatuses read the saved parameters to resume the execution of the game main processing program.