A control device is realized, which is capable of appropriately suppressing the torsional vibration of a power transmission system in response to the engagement state of an engagement device that selectively drives and couples an internal combustion engine with a rotating electrical machine. A control device (32) for controlling a rotating electrical machine that is driven and coupled with vehicle wheels by way of a power transmission mechanism, while being selectively driven and coupled with an internal combustion engine in response to the engagement state of an engagement device; wherein by executing feedback control on the basis of the rotation speed of the rotating electrical machine, it is possible to execute vibration damping control, outputting a vibration dampening torque command which suppresses the vibration due to the rotation speed of the rotating electrical machine, which is caused at least by the elastic vibration of the power transmission mechanism; and if the engagement device is in a direct engagement state, a direct connection vibration dampener controller (41) executes vibration dampening; and if the engagement device is in an indirect engagement state, an indirect connection vibration dampener controller (42) executes vibration dampening.