In　this　paper,　we　investigate　the　mixed　initial-boundary　value　problem　with　small　BV　data　for　linearly　degenerate　quasilinear　hyperbolic　systems　with　general　nonlinear　boundary　conditions　in　the　half　space　{(t,　x)　vertical　bar　t　＞=　0,　x　＞=　0}.　As　the　result　in　[A.　Bressan.　Contractive　metrics　for　nonlinear　hyperbolic　systems,　Indiana　Univ.　Math.　J.　37　(1988)　409-421]　suggests　that　one　may　achieve　global　smoothness　even　if　the　C-1　norm　of　the　initial　data　is　large,　we　prove　that,　if　the　C-1　norm　of　the　initial　and　boundary　data　is　bounded　but　possibly　large,　and　the　BV　norm　of　the　initial　and　boundary　data　is　sufficiently　small,　then　the　solution　remains　C-1　globally　in　time.　Applications　to　quasilinear　hyperbolic　systems　arising　in　physics　and　mechanics,　particularly　to　the　system　describing　the　motion　of　the　relativistic　string　in　the　Minkowski　space-time　R1+n,　are　also　given.　(C)　2008　Elsevier　Ltd.　All　rights　reserved.