Abstract: In this paper, we investigate the asymptotic behavior of global classical solutions to the mixed initial boundary value problem with small BV data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space {(t,x)|t≥0, x≥0}. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the solution approaches a combination of C¹ traveling wave solutions, provided that the C¹ norm of the initial and boundary data is bounded and the BV norm of the initial and boundary data is sufficiently small. Applications to quasilinear hyperbolic systems arising in physics and mechanics, particularly to the system describing the motion of the relativistic string in the Minkowski space-time R¹, are also given.