A hybrid vehicle drive system comprising: an engine; a rotary machine; a gear type engagement device configured to regulate rotation of the rotary machine; and a controller configured to control a vehicle to travel: in a first mode in which a reaction force of the engine is received by the engagement device of the rotary machine and the vehicle travels using the engine as a power source; or in a second mode in which the reaction force of the engine is received by the engagement device and the vehicle travels using the engine as a power source, characterized in that the controller is configured to perform a first control of receiving the reaction force of the engine by the engagement device of the rotary machine, increasing a magnitude of a torque of the rotary machine to be equal to or greater than an upper limit of an estimated torque range of the engine, and then decreasing the magnitude of the torque of the rotary machine is performed at a time the engagement device is disengaged in transition from the second mode to the first mode, and wherein a magnitude of a slope of the torque of the rotary machine at a time the magnitude of the torque of the rotary machine is decreased in the first control is equal to or less than a magnitude of a slope of a torque of the engine when the torque of the engine decreases due to explosion fluctuation of the engine. an engine; a rotary machine; a gear type engagement device configured to regulate rotation of the rotary machine; and a controller configured to control a vehicle to travel: in a first mode in which a reaction force of the engine is received by the engagement device of the rotary machine and the vehicle travels using the engine as a power source; or in a second mode in which the reaction force of the engine is received by the engagement device and the vehicle travels using the engine as a power source, characterized in that the controller is configured to perform a first control of receiving the reaction force of the engine by the engagement device of the rotary machine, increasing a magnitude of a torque of the rotary machine to be equal to or greater than an upper limit of an estimated torque range of the engine, and then decreasing the magnitude of the torque of the rotary machine is performed at a time the engagement device is disengaged in transition from the second mode to the first mode, and wherein a magnitude of a slope of the torque of the rotary machine at a time the magnitude of the torque of the rotary machine is decreased in the first control is equal to or less than a magnitude of a slope of a torque of the engine when the torque of the engine decreases due to explosion fluctuation of the engine. in a first mode in which a reaction force of the engine is received by the engagement device of the rotary machine and the vehicle travels using the engine as a power source; or in a second mode in which the reaction force of the engine is received by the engagement device and the vehicle travels using the engine as a power source, characterized in that the controller is configured to perform a first control of receiving the reaction force of the engine by the engagement device of the rotary machine, increasing a magnitude of a torque of the rotary machine to be equal to or greater than an upper limit of an estimated torque range of the engine, and then decreasing the magnitude of the torque of the rotary machine is performed at a time the engagement device is disengaged in transition from the second mode to the first mode, and wherein a magnitude of a slope of the torque of the rotary machine at a time the magnitude of the torque of the rotary machine is decreased in the first control is equal to or less than a magnitude of a slope of a torque of the engine when the torque of the engine decreases due to explosion fluctuation of the engine.