A clutch apparatus that transmits and shuts off rotary drive power of a driving shaft to a driven shaft, the clutch apparatus comprising: a plurality of clutch plates being ring shaped-flat plates placed facing a plurality of friction plates that are rotationally driven by rotary drive of the driving shaft, the plurality of clutch plates including internal teeth on inner peripheral portions of the flat plates; a center clutch coupled to the driven shaft, the center clutch including external teeth mating with the internal teeth of the clutch plate; and a pressure clutch including external teeth mating with the internal teeth of the clutch plate, the pressure clutch being configured to be placed adjacent to the center clutch in such a manner as to be displaceable in directions coming closer to and being separated from the center clutch, and press the friction plate or the clutch plate, wherein the center clutch includes a center-side end surface facing the pressure clutch, and the pressure clutch includes a pressure-side end surface facing the center clutch, the center-side end surface and the pressure-side end surface facing each other are formed flat without protrusions or indentations, each of the external teeth is arranged to form a concentric circle as each other, and included are: a protruding tooth extending as at least one of the external teeth of one of the center clutch and the pressure clutch in such a manner as to overhang the external tooth of the other clutch; and a run-off characterized in that, said run-off is configured to prevent physical interference with the protruding tooth on the external tooth of the other of the center clutch and the pressure clutch toward which the protruding tooth extends, and a part of the external tooth is omitted in the run-off, and the run-off is formed by a flat arc surface without protrusions or indentations, which is connected to two bottom lands adjacent on both side of the omitted external tooth in a circumferential direction thereof in such a manner as to be level with the bottom lands. a plurality of clutch plates being ring shaped-flat plates placed facing a plurality of friction plates that are rotationally driven by rotary drive of the driving shaft, the plurality of clutch plates including internal teeth on inner peripheral portions of the flat plates; a center clutch coupled to the driven shaft, the center clutch including external teeth mating with the internal teeth of the clutch plate; and a pressure clutch including external teeth mating with the internal teeth of the clutch plate, the pressure clutch being configured to be placed adjacent to the center clutch in such a manner as to be displaceable in directions coming closer to and being separated from the center clutch, and press the friction plate or the clutch plate, wherein the center clutch includes a center-side end surface facing the pressure clutch, and the pressure clutch includes a pressure-side end surface facing the center clutch, the center-side end surface and the pressure-side end surface facing each other are formed flat without protrusions or indentations, each of the external teeth is arranged to form a concentric circle as each other, and included are: a protruding tooth extending as at least one of the external teeth of one of the center clutch and the pressure clutch in such a manner as to overhang the external tooth of the other clutch; and a run-off the center-side end surface and the pressure-side end surface facing each other are formed flat without protrusions or indentations, each of the external teeth is arranged to form a concentric circle as each other, and included are: a protruding tooth extending as at least one of the external teeth of one of the center clutch and the pressure clutch in such a manner as to overhang the external tooth of the other clutch; and a run-off a protruding tooth extending as at least one of the external teeth of one of the center clutch and the pressure clutch in such a manner as to overhang the external tooth of the other clutch; and a run-off said run-off is configured to prevent physical interference with the protruding tooth on the external tooth of the other of the center clutch and the pressure clutch toward which the protruding tooth extends, and a part of the external tooth is omitted in the run-off, and the run-off is formed by a flat arc surface without protrusions or indentations, which is connected to two bottom lands adjacent on both side of the omitted external tooth in a circumferential direction thereof in such a manner as to be level with the bottom lands.