A slewing hydraulic work machine, comprising: a lower travelling body; an upper slewing body slewably mounted on the lower travelling body; a working device mounted on the upper slewing body and including a boom connected to the upper slewing body so as to be raisable and lowerable; a hydraulic pump (31,32) that discharges hydraulic fluid; a slewing motor formed of a variable displacement hydraulic motor that is driven by hydraulic fluid supplied from the hydraulic pump, the slewing motor configured to slew the upper slewing body in response to the supply of hydraulic fluid; a slewing control device that controls a direction and a flow rate of hydraulic fluid supplied from the hydraulic pump to the slewing motor in accordance with a slewing command operation applied to the slewing control device for slewing the upper slewing body; a boom cylinder that is operated, by hydraulic fluid supplied from the hydraulic pump, to raise and lower the boom; a boom control device that controls a flow rate of the hydraulic fluid supplied from the hydraulic pump to the boom cylinder in accordance with a boom-raising command operation applied to the boom control device for actuating the boom in a rising direction; characterised by, a boom angle detector that detects a boom angle (Theta b) that is a rising angle of the boom; and a capacity control section that controls a slewing motor capacity, which is a capacity of the slewing motor, wherein: the capacity control section includes a command motor capacity calculation section that calculates a command motor capacity, which is a command value on the slewing motor capacity (Qc), based on the boom angle detected by the boom angle detector, and a command signal input section that generates a capacity command signal corresponding to the command motor capacity and inputs the capacity command signal to the slewing motor to thereby make the slewing motor capacity be a capacity corresponding to the command motor capacity; and the command motor capacity calculation section is configured to set the command motor capacity to a predetermined base capacity (Qo) or a capacity less than the base capacity when the boom angle is equal to or less than a predetermined slewing priority angle during a performance of a slewing and boom-raising operation in which the slewing command operation is applied to the slewing control device and the boom-raising command operation is applied to the boom control device simultaneously, and configured to set the command motor capacity to a value greater than the base capacity when the boom angle is greater than the slewing priority angle during the performance of the slewing and boom-raising operation. a lower travelling body; an upper slewing body slewably mounted on the lower travelling body; a working device mounted on the upper slewing body and including a boom connected to the upper slewing body so as to be raisable and lowerable; a hydraulic pump (31,32) that discharges hydraulic fluid; a slewing motor formed of a variable displacement hydraulic motor that is driven by hydraulic fluid supplied from the hydraulic pump, the slewing motor configured to slew the upper slewing body in response to the supply of hydraulic fluid; a slewing control device that controls a direction and a flow rate of hydraulic fluid supplied from the hydraulic pump to the slewing motor in accordance with a slewing command operation applied to the slewing control device for slewing the upper slewing body; a boom cylinder that is operated, by hydraulic fluid supplied from the hydraulic pump, to raise and lower the boom; a boom control device that controls a flow rate of the hydraulic fluid supplied from the hydraulic pump to the boom cylinder in accordance with a boom-raising command operation applied to the boom control device for actuating the boom in a rising direction; characterised by, a boom angle detector that detects a boom angle (Theta b) that is a rising angle of the boom; and a capacity control section that controls a slewing motor capacity, which is a capacity of the slewing motor, wherein: the capacity control section includes a command motor capacity calculation section that calculates a command motor capacity, which is a command value on the slewing motor capacity (Qc), based on the boom angle detected by the boom angle detector, and a command signal input section that generates a capacity command signal corresponding to the command motor capacity and inputs the capacity command signal to the slewing motor to thereby make the slewing motor capacity be a capacity corresponding to the command motor capacity; and the command motor capacity calculation section is configured to set the command motor capacity to a predetermined base capacity (Qo) or a capacity less than the base capacity when the boom angle is equal to or less than a predetermined slewing priority angle during a performance of a slewing and boom-raising operation in which the slewing command operation is applied to the slewing control device and the boom-raising command operation is applied to the boom control device simultaneously, and configured to set the command motor capacity to a value greater than the base capacity when the boom angle is greater than the slewing priority angle during the performance of the slewing and boom-raising operation.