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The one-motor, two-clutch hybrid system adopted by Nissan requires high control performance for the entire system, because the single motor provides the various functions of a drive motor, generator and engine starter depending on the driving situation. An especially challenging problem is to prevent the motor torque variation caused by engine start while transmitting driving torque to the drive wheels in a situation where the engine is started in response to the driver's demand for acceleration during motor-only operation. In this case, it is effective to let the clutch on the driving side slip until engine start is completed. For that purpose, we designed the slip control system described here. This system controls driving torque by the clutch while controlling the slip speed by means of the motor speed control. The slip speed can be controlled with high accuracy because the motor speed is controlled by the motor torque which is easily controllable.