A motor vehicle (5) has a roof structure including a front roof member (6) and a rear member (4) which together form a cover for a passenger compartment (I) of the motor vehicle (5) when both of the roof members (4, 6) are in respective raised positions. When both of the roof members (4, 6) are lowered into stowed positions to form a convertible vehicle, a flap (7, 107) is deployed on each side of the motor vehicle (5) to bridge a gap between the stowed front roof member (6) and an upper edge of an outer rear panel (9).