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