A distance device bridges a free space between a carrier part and a roof body for fastening a roof luggage rack, such as a roof rail, a roof strip or the like, on a vehicle roof by a threaded screw, with a support part and a counter support part. The support part and counter support part are held together by a threaded connection and can be adjusted relative to each other in order to set a bridging length. The support part or counter support part is carried along by a rotationally engaging connection with the threaded screw when it is screwed into a counter thread of the roof luggage rack or carrier part as far as a contact position with the carrier part or the roof body. The rotationally engaging connection has a plastic carrier into which the thread of the threaded screw is/has been screwed for carrying along with frictional resistance.