Abstract. This paper shows that the solutions to the nonlinear perturbed differential systemhave bounded properties. To show these properties, we impose conditions on the perturbed part t t 0 g(s, y(s), T1y(s))ds, h(t, y(t), T2y(t)), and on the fundamental matrix of the unperturbed system y = f (t, y) using the notion of h-stability.