The mechanism has a two-part drive carriage (10), the first part (12) always being connected to a motor-driven flexible drive-belt (17) guided along a guide-rail (13). The second part (11) is connected to the door. Both parts are locked and unlocked together by a coupling possessing a catch (28). The catch is especially in the form of a sprung stop-bolt, on one of the drive carriages and snapping into an indent (33) on the other carriage part. A second indent (35) is in a staggered position in relation to the first indent in the direction (B) in which the drive-carriage moves to open. The second indent has a slide part enabling the catch fitting into the second indent to be displaced into the first indent.