Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 78, pp. 1-11. Title: Existence and uniqueness of solutions for a second-order nonlinear hyperbolic system Author: Rodica Luca (Gh. Asachi Technical Univ., Iasi, Romania) Abstract: We study the existence, uniqueness and asymptotic behaviour of solutions to a second-order nonlinear hyperbolic system of equations. The spatial variable is in the positive half-axis. Submitted May 20, 2010. Published June 20, 2011. Math Subject Classifications: 35L55, 47J35, 47H05. Key Words: Hyperbolic system; boundary conditions; Cauchy problem; monotone operator; strong solution; weak solution.