In this paper, we present a mechanism, called oscillation killer, intended to eliminate limit cycles that may occur as a consequence of unexpected external disturbances, interactions with the environment, changes in systems set-points, physical parameters, and so on. Examples range from controlled systems with friction to electrical networks with varying loads and impedances. The proposed mechanisms is shown to be particulary appropriate for nonlinear systems displaying a locally asymptotically equilibrium point surrounded by a locally asymptotically stable limit set outside this local domain.