A control device controlling a hybrid vehicle drive apparatus that includes an internal combustion engine, a rotary electric machine drivingly connected to a wheel and a clutch selectively drivingly connecting the internal combustion engine with the rotary electric machine. The control device performs control such that, when a start request of the internal combustion engine is issued in the state in which the clutch is released and combustion of the internal combustion engine is stopped, a rotational speed of the internal combustion engine is raised to a rotational speed of the rotary electric machine by transmitting driving torque of the rotary electric machine to the internal combustion engine by increasing a torque transfer capacity of the clutch, and, after the rotational speed of the internal combustion engine is synchronized with the rotational speed of the rotary electric machine, the combustion of the internal combustion engine is started.