This　work　is　a　continuation　of　our　previous　work,　in　the　present　paper　we　study　the　generalized　nonlinear　initial-boundary　Riemann　problem　with　small　BV　data　for　linearly　degenerate　quasilinear　hyperbolic　systems　of　conservation　laws　with　nonlinear　boundary.　conditions　in　a　half　space　{(t,　x)　vertical　bar　t　＞=　0,　x　＞=　0}.　We　prove　the　global　existence　and　uniqueness　of　piecewise　C(1)　solution　containing　only　contact　discontinuities　to　a　class　of　the　generalized　nonlinear　initial-boundary　Riemann　problem,　which　can　be　regarded　as　a　small　BV　perturbation　of　the　corresponding　nonlinear　initial-boundary　Riemann　problem,　for　general　n　x　n　linearly　degenerate　quasilinear　hyperbolic　system　of　conservation　laws:　moreover,　this　solution　has　a　global　structure　similar　to　the　one　of　the　self-similar　solution　u　=　U(x/t)　to　the　corresponding　nonlinear　initial-boundary　Riemann　problem.　Some　applications　to　quasilinear　hyperbolic　systems　of　conservation　laws　arising　in　the　string　theory　and　high　energy　physics　are　also　given.　(C)　2011　Elsevier　Inc.　All　rights　reserved.