In　the　present　paper　the　author　investigates　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　shocks　and　contact　discontinuities,　the　perturbations　are　in　BV　but　they　are　assumed　to　be　C-1　smooth,　with　bounded　and　possibly　large　C-1-norms.　The　author　obtains　the　almost　global　existence　and　lifespan　of　classical　discontinuous　solutions　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　compressible　Euler　equations,　are　also　given.