A non-limiting example information processing apparatus that functions as a game apparatus includes a first LCD and a second LCD, and usually, a game screen of a single-play game is displayed on the first LCD and a list screen is displayed on the second LCD. The list screen displays at least an icon of a player of another game apparatus capable of performing a communication with the information processing apparatus. In addition, icons of a player who is registered in the game apparatus as a friend and a player who is determined as an acquaintance are also displayed whether a communication can be performed. By performing a communication with using the game apparatus with a passer-by player with whom no communication has been performed, for example, the player is automatically determined as an acquaintance player.