This　paper　is　concerned　with　the　asymptotic　behavior　of　global　classical　solutions　of　diagonalizable　quasilinear　hyperbolic　systems　with　linearly　degenerate　characteristic　fields.　On　the　basis　of　the　existence　result　for　the　global　classical　solution,　we　prove　that　when　t　tends　to　the　infinity,　the　solution　approaches　a　combination　of　C1　traveling　wave　solutions,　provided　that　the　C1　norm　and　the　BV　norm　of　the　initial　data　are　bounded　but　possibly　large.　In　contrast　to　former　results　obtained　by　Liu　and　Zhou　[J.　Liu,　Y.　Zhou,　Asymptotic　behaviour　of　global　classical　solutions　of　diagonalizable　quasilinear　hyperbolic　systems,　Math.　Methods　Appl.　Sci.　30　(2007)　479500],　ours　do　not　require　their　assumption　that　the　system　is　rich　in　the　sense　of　Serre.　Applications　include　that　to　the　one-dimensional　BornInfeld　system　arising　in　string　theory　and　high　energy　physics.　©　2010　Elsevier　Ltd.　All　rights　reserved.