The convertible car has side doors and a passenger space with an integral, rigid roof, enclosing it completely apart from an oblong recess for the driver, roughly at the level of the open body belt line. A low windscreen encloses the front and sides of the recess. The plastics cover (19) is joined by hinges to the body (2), and secured to the latter in the closed position by detachable locks. The roof is pref. movable to an inclined rear position.