The invention relates to a device for controlling start clutches of vehicles. The device for controlling start clutches of the vehicles is configured so that the torque output by the engine is input to a torque converter which is provided with a pump impeller and a turbine and the torque is output from the torque converter via the start clutch to a drive wheel, stops an engine and releases the start clutch by way of predetermined conditions being satisfied and restarts the stopped engine and engages the clutch by way of prescribed predetermined return conditions being satisfied while the vehicle is running. The device for controlling start clutches of the vehicles is configured so as to estimate the turbine torque in the torque converter on the basis of the engine speed, the capacity factor of the torque converter and the torque ratio, and to increase the transmitting torque capacity of the clutch according to the estimated torque of the turbine, and after the clutch is engaged, to estimate the turbine torque on the basis of the amount of air taken in by the engine and the engine speed, and to control the transmitting torque capacity of the clutch according to the estimated torque when there is a demand for increased engine output when restarting the engine.