A top for a convertible has a linkage with which a plurality of roof sections can be displaced between a closed position and an open position. The rearmost roof section is configured as a rear window frame, and the linkage has a control link which is mounted pivotally on a bracket which can be fastened or is fastened to the vehicle. The linkage has a clamping hoop and a coupling linkage for controlling the kinematics of the rear window frame, said coupling linkage having a front coupling link and a rear coupling link which are mounted pivotally on the clamping hoop and on the rear window frame. In order to stabilize the top in its end positions, for the rear coupling link, there is formed on the clamping hoop a front stop against which the rear coupling link bears when the top is closed, and a rear stop against which the rear coupling link bears when the top is open.