In　this　paper,　we　consider　the　mixed　initialboundary　value　problem　for　first-order　quasilinear　hyperbolic　systems　with　general　nonlinear　boundary　conditions　in　the　half　space　{(t,　x)　|　t　<　0,　x　<　0}.　Based　on　the　fundamental　local　existence　results　and　global-in-time　a　priori　estimates,　we　prove　the　global　existence　of　a　unique　weakly　discontinuous　solution　u　=　u(t,　x)　with　small　and　decaying　initial　data,　provided　that　each　characteristic　with　positive　velocity　is　weakly　linearly　degenerate.　Some　applications　to　quasilinear　hyperbolic　systems　arising　in　physics　and　other　disciplines,　particularly　to　the　system　describing　the　motion　of　the　relativistic　closed　string　in　the　Minkowski　space　R1+n,　are　also　given.　©　2009　World　Scientific　Publishing　Company.