A vehicle roof has at least one roof part coupled to a body-side roof kinematic system to be adjustable between a closed position covering the vehicle interior and a storage position. A cover with a pivoting mount is attached to the roof kinematic system through a coupling kinematic system. The coupling kinematic system includes a connecting link that makes a swinging connection with the cover. The connecting link passes through a lined-up position when the roof is moved between its closed and storage positions. The cover swings about a body-side joint. The coupling kinematic system exclusively includes links coupled through joints. There are no more than three links in the kinematic transmission path between the cover and the roof kinematic system.