In　this　paper,　we　study　the　global　structure　stability　of　the　Riemann　solution　u　=　U(x/t)　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　under　a　small　BV　perturbation　of　the　Riemann　initial　data.　We　prove　the　global　existence　and　uniqueness　of　piecewise　C(1)　solution　containing　only　n　contact　discontinuities　to　a　class　of　the　generalized　Riemann　problem,　which　can　be　regarded　as　a　small　BV　perturbation　of　the　corresponding　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　Riemann　problem.　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　possesses　a　global　nonlinear　structure　stability　under　a　small　BV　perturbation　of　the　Riemann　initial　data.　Some　applications　to　quasili　near　hyperbolic　systems　of　conservation　laws　arising　in　physics,　particularly　to　the　system　describing　the　motion　of　the　relativistic　string　in　Minkowski　space　R(1+n),　are　also　given.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.