A cooking appliance (5) includes an outer cabinet (15) within which is provided an oven cavity (10) which can be selectively accessed by movement of a door (25) mounted through a door linkage system (75, 85, 90, 100, 120, 125) which enables the door (25) to be shifted between opened and closed positions through either sliding or tilting movements. In particular, the door (25) can be automatically or manually shifted between open and closed positions, through either the sliding or tilting motions. In accordance with another aspect of the invention, the door (25) can be automatically opened at the end of a process or cooking cycle, or manually opened.