In this paper, we consider the cluster consensus problem in delayed directed networks where agents are described by second-order discrete-time dynamics. Unlike first order systems, delay is shown to lead to instability in second order systems if the controller parameters are not chosen properly. Furthermore, the numerical results reveal that as the amount of delay increases, the stability region in the controller parameter space shrinks. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.