A hard-top vehicle is provided with a roof structure which includes a roof part and a rear-window part connected pivotably thereto. The roof structure is lowered from a closed position, in which it bears in the region of a front windscreen frame and covers the rear-passenger-compartment region, into an open position, towards the tail-end region of the vehicle, via a positive-control device. The positive control device is supported in the tail-end region of the vehicle bodywork and can be pivoted about a tail-end pivot pin fixed to the vehicle, into a folding-top compartment. The positive-control device includes at least one control element which is connected in a rotationally fixed manner to the roof part in the region of a roof pivot pin. In this arrangement, the control element is designed as a linkage which acts on a guide part, in the region of the roof pivot pin, with a guide rod and a main guide rod.