When a piece 7 and a sleeve 8 are engaged with each other, an engagement device 1 controls an actuator 9 to move the sleeve 8 in a direction approaching the piece 7 with the piece 7 rotating in a negative rotation direction (a direction in which small tooth surfaces 11a of dog teeth 11 of the piece 7 and small tooth surfaces 12a of dog teeth 12 of the sleeve 8 face and approach each other) relative to the sleeve 8, and further controls a first motor generator MG1 to change the rotation speed of the piece 7 from a negative rotation speed to zero or more after a predetermined stroke condition for the movement of the sleeve 8 relative to the piece 7 is satisfied. Accordingly, it is possible to reliably perform the engagement and improve the durability.