A convertible vehicle top displaceable between closed and storage positions, and which has a top linkage, which, on both sides with respect to a vertical longitudinal center plane of the vehicle, may extend through a linkage exit opening of a vehicle trim when the top is in the closed position, each of the linkage exit openings on both sides being provided with a cover, the cover having a panel which can be displaced between a cover position, in which it covers the linkage exit opening, and an open position, in which the linkage exit opening is open. Each cover can have a guiding device, which guides the respective panel on a curved track in the direction of the vehicle front and outward in the transverse direction with respect to the vertical longitudinal center plane of the vehicle when the panel is displaced from the cover position into the open position.