Summary: The aim of the paper is to discuss the existence of maximal and minimal solutions of a nonlinear nonlocal hyperbolic differential problem. A monotone iterative technique, considered in [G. S. Ladde, V. Lakshmihantham and A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations (1985; Zbl 0658.35003)], is used to prove this result.