A convertible vehicle top, having a top cover and a top linkage displaceable between a closed position, and a storage position, the top linkage having a link assembly on either side of a vertical longitudinal center plane of the top, each link assembly having two main links pivotably mounted on a main bearing attachable to a vehicle body and which form a multi-bar linkage together with a roof middle link, and the top linkage having transverse bows via which the two link assemblies are connected. The link assemblies may each have a fabric deflection lever which is pivoted into a straightened position by the top cover when the top is in the closed position and which is pivoted into a bent position in such a manner that the top cover is deflected around the free end of the deflection lever when the top is in the storage position.