This　work　is　a　continuation　of　our　previous　work　[Z.Q.　Shao,　Global　structure　stability　of　Riemann　solutions　for　linearly　degenerate　hyperbolic　conservation　laws　under　small　BV　perturbations　of　the　initial　data,　Nonlinear　Anal.　Real　World　Appl.　11　(2010)　3791-3808].　In　the　present　paper　we　investigate　the　global　structure　stability　of　Riemann　solutions　for　general　quasilinear　hyperbolic　systems　of　conservation　laws　under　small　BV　perturbations　of　the　initial　data,　where　the　Riemann　solution　only　contains　the　shocks　and　contact　discontinuities,　and　at　least　a　shock　wave.　The　perturbations　are　in　BV　but　they　are　assumed　to　be　C(1)-smooth,　with　bounded　and　possibly　large　C(1)-norms.　We　get　a　lower　bound　of　the　lifespan　of　the　piecewise　C(1)　solution　to　a　class　of　the　generalized　Riemann　problem,　which　can　be　regarded　as　a　small　BV　perturbation　of　the　corresponding　Riemann　problem.　Some　applications　to　quasilinear　hyperbolic　systems　of　conservation　laws　arising　in　physics,　particularly　to　one-dimensional　Euler　equations　of　gas　dynamics　for　a　compressible,　inviscid,　non-heat　conducting　gas　in　Eulerian　coordinates,　are　also　given.　(C)　2011　Elsevier　Inc.　All　rights　reserved.