We　extend　Hartman＇s　linearization　theorem　to　the　uniformly　asymptotic　stable　and　unbounded　case.　We　get　the　following　conclusion:　there　is　a　constant　δ　＞　0　such　that　the　nonlinear　system　frac(d　x,　d　t)　=　A　(t)　x　+　f　(x,　t)　and　its　linear　part　frac(d　x,　d　t)　=　A　(t)　x　are　topologically　equivalent　if　the　linear　system　is　uniformly　asymptotically　stable　and　f　(x,　t)　satisfies　Lipschitz＇　condition　with　constant　δ.　©　2005　Elsevier　Ltd.　All　rights　reserved.