A slewing hydraulic work machine includes a slewing control device performing a slewing control in accordance with an applied slewing command operation, a boom control device performing a boom-raising control in accordance with an applied boom-raising command operation, a boom angle detector, and a capacity control section. The capacity control section calculates a command motor capacity based on a boom angle, generates a capacity command signal corresponding to the command motor capacity and inputs the signal to a slewing motor. During the performance of slewing and boom-raising operation, the capacity control section sets the command motor capacity to a value equal to or less than a base capacity when the boom angle is equal to or less than a slewing priority angle and sets the command motor capacity to a value greater than the base capacity when the boom angle is greater than the slewing priority angle.