To reduce energy required for continuously connecting input/output elements, while maintaining the function of a slip control type clutch capable of fine-adjusting an engaging force.

This compound clutch device transmits power between input/ output elements 11 (11a, 11b) and 12, using a fractional force caused by pressing plates 3 and 4 of a multiple disk clutch 1. When the input/output elements 11 (11a, 11b) and 12 are engaged with each other, because the multiple disk clutch 1 is engaged earlier than a roller clutch 2, the input/output elements 11 (11a, 11b) and 12 are engaged with each other, using the roller clutch 2 requiring less energy for continuously engaging these elements 11 (11a, 11b) and 12 with each other. Thus, the engagement of the multiple disk clutch 1 requiring a large amount of energy for pressing the plates 3 and 4 takes less time until the engagement of the roller clutch 2 is completed. Then, the energy required for continuously engaging the input/output elements 11 (11a, 11b) and 12 can be reduced, while maintaining the function of the multiple disk clutch 1 capable of fine-adjusting an engagement force.