Roof construction for motor vehicles

A roof structure for motor vehicles has at least one roof panel attached to the body of the motor vehicle, a headliner, a linkage for shifting the roof panel from an out-of-service position into a use position, and at least one support element carrying a portion of the headliner for displacement between an out-of-service end position and a working end position. The headliner portion in the respective out-of-service end position covers a motor-vehicle portion and in the working position frees the motor-vehicle portion. The support element is pivotal to displace the portion about a pivot axis fixed relative to the roof panel.