obtained results concerning the perturbation of the eventual uniform asymptotic stability (abbreviated by EvUAS). They considered (E) x'-f(t, x) (P-l) y'--f(t, y)-b g(t, y) (P-2) y'-f(t, y) + h(t) (P-3) y'-f(t, y) qg(t, y) + h (t) under the condition that f(t, x) satisfies the Lipschitz condition and g(t,x) and h(t) satisfy various conditions. In this note we consider these problems under the generalized Lipschitz conditions.