A slewing-type working machine, comprising: a base carrier; an upper slewing body mounted on the base carrier so as to be capable of being slewed; a slewing motor which is a hydraulic motor adapted to be operated by receiving supply of hydraulic fluid to drive the upper slewing body to slew the upper slewing body; a variable-displacement-type hydraulic pump which supplies the hydraulic fluid to the slewing motor; a pump regulator which varies a discharge flow rate of the hydraulic pump; a slewing operation device including an operation member to which an operation is applied to input a command regarding the driving for slewing, the operation device adapted to output an operation signal corresponding to the operation applied to the operation member; a control valve which is operated to control supply of the hydraulic fluid to the slewing motor and discharge of the hydraulic fluid from the slewing motor, based on the operation signal of the slewing operation device; a relief valve which returns, to a tank, the excess of the hydraulic fluid discharged from the hydraulic pump; a motor-rotational-speed detector adapted to detect a rotational speed of the slewing motor; and a controller adapted to command the discharge flow rate of the hydraulic pump to the pump regulator, characterized in that the slewing-type working machine comprises an operation detector (28, 29) adapted to detect a direction and an amount of the operation applied to the operation member of the slewing operation device; and the controller is adapted to obtain a deviation (α) between a target rotational speed of the slewing motor obtained from the amount of the operation applied to the operation member of the slewing operation device and an actual rotational speed (nr) of the slewing motor detected by the motor rotational speed detector, that is, a value corresponding to an excess flow rate which is a flow rate of the excess hydraulic fluid, and to control the discharge flow rate of the hydraulic pump so as to make the deviation (α) closer to 0. a base carrier; an upper slewing body mounted on the base carrier so as to be capable of being slewed; a slewing motor which is a hydraulic motor adapted to be operated by receiving supply of hydraulic fluid to drive the upper slewing body to slew the upper slewing body; a variable-displacement-type hydraulic pump which supplies the hydraulic fluid to the slewing motor; a pump regulator which varies a discharge flow rate of the hydraulic pump; a slewing operation device including an operation member to which an operation is applied to input a command regarding the driving for slewing, the operation device adapted to output an operation signal corresponding to the operation applied to the operation member; a control valve which is operated to control supply of the hydraulic fluid to the slewing motor and discharge of the hydraulic fluid from the slewing motor, based on the operation signal of the slewing operation device; a relief valve which returns, to a tank, the excess of the hydraulic fluid discharged from the hydraulic pump; a motor-rotational-speed detector adapted to detect a rotational speed of the slewing motor; and a controller adapted to command the discharge flow rate of the hydraulic pump to the pump regulator,