A planetary differential reducer using internal gears with small tooth number difference is described : Essential points of the design are considered and an example of the reducer is manufactured. The idea is used that an internal gear with small tooth number difference has theoretically a contact ratio less than unity owing to trochoidal interference, but it is practically available under suitable condition. In case that the tooth number difference of the input-side gears is not the same as that of the output-side, such an especially high reduction ratio as 1/10, 000 is obtained. The calculation methods for strength and efficiency are given and the experimental value of efficiency is shown to agree with the theoretical one. The cost down of reducers with high reduction ratio is expected from using the above reducers which can be easily manufactured with standard pinion cutters of pressure angle 20°.