We study passive and nonlinear targeted energy transfers induced by resonant interactions between a single-degree-of-freedom nonlinear energy sink and a flexible swept wing. With a series of ground vibration tests, we show that the nonlinear energy sink can be designed to quickly and efficiently absorb energy from one or more wing modes in a completely passive manner. Results indicate that it is feasible to use such a device to suppress or prevent aeroelastic instabilities like limit-cycle oscillations. The design of a compact nonlinear energy sink is introduced and the parameters of the device are examined experimentally, confirming that the required nonlinearizable stiffness is achieved. Ground vibration experiments performed on the wing-nonlinear energy sink system indicate that targeted energy transfer is achievable resulting in a significant reduction in the second bending mode response of the wing.