An in-flight refueling system, damping device and method are provided for substantially reversing a change in the disposition of an elongate hose extending from a first aircraft during an in-flight refueling operation. The various embodiments of the present invention provide a compact, lightweight, and easily installed damping device that may act to minimize the occurrence of oscillations within the elongate hose that may act to produce a change in the disposition of the elongate hose. In addition, the embodiments of the present invention facilitate the detuning of the elongate hose and, for instance, an attached drogue that may oscillate uncontrollably at a resonant frequency in response to aerodynamic forces exerted on the hose and drogue during an in-flight refueling operation.