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. Furthermore, highly accurate driving torque is achieved without using a sensor. This is possible because the control system can use feedback control by estimating the driving torque from various information about the vehicle.Bench and driving tests were conducted to evaluate the effectiveness of this control system. The experimental results showed that the slip speed and the driving torque tracked the respective target well. The results also showed that the control system achieved smooth vehicle acceleration with little vibration when the engine was started in response to the driver's demand for acceleration during motor-only operation.