In this paper, we investigate bounds for solutions of nonlinear perturbed functional difierential systems. Integral inequalities play a vital role in the study of boundedness and other qualitative properties of solutions of difierential equations. The method incorporating integral inequalities takes an important place among the methods developed for the qualitative analysis of solutions to linear and nonlinear system of difierential equations. As is traditional in a pertubation theory of nonlinear difierential equations, the behavior of solutions of a perturbed system is determined in terms of the behavior of solutions of an unperturbed system. There are three useful methods for showing the qualitative behavior of the solutions of perturbed nonlinear system : Lyapunov's second method, the use of integral inequalities , and the method of variation of constants formula. In the presence the method of integral inequalities is as e-cient as the direct Lyapunov's method. Pinto (15,16) introduced h-stability (hS) with the intention of obtain- ing results about stability for a weakly stable system (at least, weaker than those given exponential asymptotic stability) under some pertur- bations. That is, Pinto extended the study of exponential asymptotic stability to a variety of reasonable systems called h-systems. Using this notion, Choi and Ryu(3,4) investigated bounds of solutions for nonlinear perturbed systems and nonlinear functional difierential systems. Also, Goo et al.(8,11) studied the boundedness of solutions for nonlinear func- tional perturbed systems.