A hydraulic system for steering an aircraft while taxiing selectively applies pressurized fluid to different ports of a hydraulic motor to turn a landing gear wheel either left or right. Shimmy of the landing gear attached to the wheel is dampened by a device that is coupled across the hydraulic lines that are connected to the motor. That device has a piston in a bore with one hydraulic line connected via an orifice to a first chamber on one side of the piston and the other hydraulic line connected via a different orifice to a second chamber on the other side of the piston. The piston stroke is limited to control the effective oscillation damping amplitude. The shimmy produces an oscillating pressure differential in the two hydraulic lines which is dampened by the device.