A control device for a vehicular drive system including (a) a differential mechanism operable to distribute an output of an engine (8) to a first electric motor and a power transmitting member, (b) a second electric motor disposed in a power transmitting path between the power transmitting member and a drive wheel of a vehicle, and (c) a differential-state switching device operable to place the differential mechanism selectively in one of a differential state in which the differential mechanism is operable to perform a differential function and a locked state in which the differential mechanism is not operable to perform the differential function, the control device including an engine-stop switching control portion operable to control the differential-state switching device to place the differential mechanism in the differential state, upon stopping of the engine, so that the engine speed can be rapidly lowered to zero by controlling the first electric motor in the differential state of the differential mechanism, so as to reduce a possibility of occurrence of a resonance phenomenon of the drive system and a resultant vibration of the vehicle when the engine is stopped.