[Subject] In a hybrid drive power apparatus, distortional oscillation of power transfer shafts caused by fluctuation in output torque of an engine is restrained to prevent the occurrence of unpleasant noises such as hitting noise of gear teeth, harsh noise in the vehicle body and the like.[Solution] In 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 for establishing a first drive train, 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 for establishing a second drive train, a motor-generator in drive connection with the first input shaft or the second input shaft, and a driven mechanism to be driven by the drive power transmitted from an output shaft of the first gear-shift mechanism or from an output shaft of the second gear-shift mechanism, the motor-generator is activated as an electric motor when amplitude of fluctuation in rotation speed of the engine detected by a sensor increases more than a preset upper limit value of amplitude thereby to apply load torque in reverse phase relative to the fluctuation in rotation speed to the engine at the same period as that of the fluctuation in rotation speed.