Abstract: An apparatus for mounting a tire on a rim and removing it therefrom has a device for rotating the rim, which is embodied as a pneumatic motor having a rotor and a stator with radially arranged piston/cylinder units and cams disposed on a circle, a device for firmly holding the rim of self-centering arms that are pivotable via the pneumatic motor, a device for forcing the bead edges of the tire into the rim bed that comprises rollers acting simultaneously on both beads, and a device for pulling the bead edges from or onto the rim, with an element for bracing against the wheel flange. Via the hydraulic motor that drives the arms of the holding or chucking device, a rim is firmly held and once it is firmly clamped is rotated via the motor. The apparatus is operated completely pneumatically.