A control device is provided for a vehicle drive apparatus, which includes a differential mechanism distributing an output of an engine to a first electric motor and an output shaft, and an electric motor provided on the output shaft, for miniaturizing the drive apparatus and/or providing improved fuel economy while preventing switching shocks from occurring in starting or stopping the engine. A switching clutch C0 or switching brake B0 is provided for placing a shifting mechanism 10 in a continuously variable shifting state and a step-variable shifting state, enabling the vehicle drive apparatus to have combined advantages including a fuel economy improving effect of a transmission, enabled to electrically change a speed ratio, and a high transmitting efficiency of a gear type transmitting device enabled to mechanically transmit drive power. During the occurrence of overlapping phases between operation of switching control mean 50 for switching a shifting state and operation of engine starting and stopping control means 90 for starting or stopping the engine, execution control means 82 enables the operations to be sequentially executed so as to avoid overlapping executions, thereby suppressing the switching shocks.