[Subject]In a hybrid drive power apparatus, loss of drive power caused by drag torque of a friction clutch is decreased to reduce fuel consumption rate.[Solution]A hybrid drive power apparatus of the type which comprises a first gear-shift mechanism assembled with a first input shaft to be applied with drive power from an engine through a first friction clutch, a second gear-shift mechanism assembled with a second input shaft to be applied with the drive power of the engine through a second friction clutch, a motor-generator in drive connection with the second input shaft, a final output shaft in drive connection with each output shaft of both the gear-shift mechanisms, and a driven mechanism to be driven by drive power transferred from the final output shaft, wherein drive torque of the motor-generator activated as an electric motor is transferred to the final output shaft through a gear set as a shift step selected in the second gear-shift mechanism, wherein the hybrid drive power apparatus includes control means for activating the motor-generator as the electric motor in a condition where the first friction clutch is brought into engagement to transfer drive torque of the engine to the final output shaft through the first input shaft and the first gear-shift mechanism and for engaging the second friction clutch after activation of the motor-generator so that the final output shaft is applied with drive torque of the motor-generator activated as the electric motor and the drive torque of the engine through the first input shaft and the first gear-shift mechanism.