A control device for hybrid vehicle drive apparatus is disclosed. Upon receipt of a start-up request on an engine (8), if a determination is made that a rattling gear noise in a power distributing mechanism (16) exceeds a given value, first and second clutches (C1 and C2) are disengaged to cause a power transmitting path to be placed in a power interrupting state, and the first and second clutches (C1 and C2) are engaged to cause the power transmitting path to be placed in a non-differential state. Thus, engine start-up is initiated. This allows the engine (8) to be started up with a limited occurrence of rattling between gears incorporated in the power distributing mechanism (16) with a reduction in rattling gear noise.