A control device is provided and avoids the occurrence of torque level differences when the direction of the relative rotation between an internal combustion engine and a dynamo-electric machine is reversed during the start-up of the internal combustion engine with a shift engaging device in a directly-engaged state. This control device is for a vehicle drive device in which a transmission engaging device, a dynamo-electric machine, and a transmission are provided to a power transmission path connecting an internal combustion engine and wheels. This control device maintains the transmission ina non-slip state at the time of executing internal combustion engine starting control, and, during a period before the completion of the transition of the transmission engaging device from a slip engaged state to a directly-engaged state, reduces the engagement pressure of the transmission engaging device so that the transmission torque of the transmission engaging device becomes zero at the relative rotation direction reversing time (T04) when the rotational speed (Ne) of the internal combustion engine is higher than the rotational speed (Nin) of the dynamo-electric machine.