Tire assembly for a bicycle rim, including a wheel tire with a tread surface and two tire beads, an inner tire disposed within the wheel tire, a tube disposed within the inner tire, and a valve arrangement for filling the tube and an intermediate space between the rim and the wheel tire with different air pressures. The inner tire in the filled and mounted condition bears on the tire beads of the wheel tire and presses the beads against the rim. The inner tire has a first through opening which in the mounted condition communicates with the intermediate space, and an insert part disposed between the rim and the tube and between the tube and the inner tire. The insert part forms an air duct between the rim and the tube and between the tube and the inner tire up to the through opening in the inner tire.