A control apparatus for a hybrid vehicle drive system including (a) an engine, (b) an electrically controlled differential portion having an input shaft connected to the engine, an output shaft, a differential mechanism, and an electric motor which is operatively connected to a rotary element of the differential mechanism and an operating state of which is controlled to control a differential state between rotating speeds of the input and output shafts, (c) a hydraulically operated automatic transmission portion which constitutes a part of a power transmitting path between the electrically controlled differential portion and a drive wheel of a hybrid vehicle, (d) a hydraulic control unit for controlling the hydraulically operated automatic transmission portion, (e) a mechanical oil pump operable by the engine to deliver a pressurized working fluid to the hydraulic control unit, and (f) an electric oil pump electrically operated independently of the mechanical oil pump, to deliver a pressurized working fluid to the hydraulic control unit, the control apparatus including a hybrid-drive-system starting portion configured to operate the engine, upon starting of the hybrid vehicle drive system, for operating the mechanical oil pump to deliver the pressurized working fluid of a predetermined pressure to the hydraulic control unit.