Abstract: A closure system for a sliding main door and a sliding screen door system of the type typically used in houses and some commercial buildings operates to permit three modes of operation of the sliding screen door and the sliding main door relative to one another. In a first mode of operation handles on the doors freely pass by one another and the two doors may be operated completely independently of one another. The handle on the sliding screen door is capable of movement to different vertical positions; and in another position, cooperating surfaces on the two handles cause the sliding screen door always to be closed when the main door is closed. When the main door is opened, however, the sliding screen door in this mode is capable of movement back and forth independently of the main door to the extent of the opening of the sliding main door.