A game apparatus includes, for example, a CPU, and a ROM and/or a RAM for executing and storing game programs and game program backup data. The RAM has multiple pre-allocated backup game data storage areas for use by different game programs during their respective execution including a single-player game backup data area, a multi-player game backup data area and a shared backup data storage area. The shared backup data storage area is provided for storing information that is accessible in common by a plurality of games, and separate game backup data storage areas are provided for each of the single-player version of a game and the multi-player version of a game. If a predetermined game condition is accomplished during progress of a game by an operator playing one of the plurality of stored game programs, the CPU writes information relating to the accomplished condition to the shared backup data storage area and to the backup data storage areas for both the single-player game version and the multi-player game version corresponding to the particular game in progress in which the condition was accomplished.