This　work　is　a　continuation　of　our　previous　work.　In　the　present　paper　we　study　the　global　structure　stability　of　the　Riemann　solution　u　=　U(x/t)　containing　only　contact　discontinuities　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　presence　of　a　boundary.　We　prove　the　existence　and　uniqueness　of　a　global　piecewise　C-1　solution　containing　only　contact　discontinuities　to　a　class　of　the　generalized　Riemann　problems　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　a　half　space.　Our　result　indicates　that　this　kind　of　Riemann　solution　u　=　U(x/t)　mentioned　above　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　presence　of　a　boundary　possesses　a　global　nonlinear　structure　stability.　Some　applications　to　quasilinear　hyperbolic　systems　of　conservation　laws　occurring　in　physics　and　other　disciplines,　particularly　to　the　system　describing　the　motion　of　the　relativistic　string　in　Minkowski　space　R1+n,　are　also　given.