PURPOSE: To simplify the structure of an oil-pressure circuit as well as reduce the cost by a method in which oil pressure during the steady slewing period of a construction machine having a slewing function is supplied to the other working machine to shorten the cycle time of the working machine.

CONSTITUTION: An oil-pressure motor 3 for slewing is connected to an oil-pressure pump 1 through a valve 2 for slewing provided with a neutral position 2a and normal and reverse slewing positions 2b and 2c and capable of performing switch operations by a pilot pressure from a pilot valve 6 to make up a slewing oil-pressure circuit. When the valve 6 is operated and the motor 3 is turned normally or reversely, the amount of oil flowing in the motor 3 is increased, the valve 2 is restored to the neutral position 2a, and the flow rate becomes maximum. Since the motor 3 is in inertial movement in the steady turning state, the oil discharged from the pump 1 is not supplied to the slewing circuit but to the other working machine, e.g., boom, etc.