A hybrid vehicle drive apparatus, including a prime-mover-output-shaft, a transmission-input-shaft and a motor-rotor provided therebetween, each rotatable around an axis-line, a first-clutch connecting/disconnecting the output-shaft and the motor, a second-clutch connecting/disconnecting the motor and the input-shaft, a case-member having a radially extending non-rotating-sidewall-member and a non-rotating-shaft-member extending around the axis-line, and a rotor-support-member having a rotating-shaft-member rotatably fitted on the non-rotating-shaft-member and a rotating-sidewall-member facing the non-rotating-sidewall-member and extending radially outward from the rotating-shaft-member, and cantilevering the rotor, wherein the first/second-clutch has first/second-plates alternately and rotatably arranged in the axial-direction, a clutch-hub supporting the first-plates movably in the axial-direction, and a clutch-drum supporting the second-plates movably in the axial-direction, the clutch-hub of the first-clutch is integrally rotatable with the output-shaft, the clutch-hub of the second-clutch is integrally rotatable with the input-shaft, and the clutch-drums of the first/second-clutches are a single-shared-clutch-drum and integrally rotatable with the rotor-support-member.