During a sleep mode, if an input made via operation switches matches a resume condition, a portable game apparatus cancels the sleep mode and generates a resume window. Next, a timer which counts down a predetermined length of time is set off, and the resume window is displayed on an LCD. Then, if an instruction from a user instructs a resume from the sleep mode, the resume window is erased, and game data and a game image which existed immediately before entering the sleep mode are restored, and the normal game processing is resumed. On the other hand, if inactivity for the predetermined length or longer with respect to the operation switches is detected, or if an option of not choosing to resume has been selected by the user, the sleep mode is again entered.