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)　|　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　C1　norm　of　the　initial　data　is　large,　we　prove　that,　if　the　C1　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　C1　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.　©　2008　Elsevier　Ltd.　All　rights　reserved.