Abstract: Due to the limitation of the closed-form analysis of end-to-end delay in mobile ad hoc networks, this paper develops an effective modeling scheme for delay in the networks where the delivery is out-of-order and the two-hop relay algorithm with single copy is involved, and presents a rigorous theoretical upper bound. First, for various random mobility models, it is proved that the inter-meeting time between mobile nodes can be expressed in a unified expression. Furthermore, taking the medium competition, the traffic competition and the queuing delay into consideration, the critical time period of delay is defined accurately, and then the queuing service is modeled. Finally, an exact upper bound of the end-to-end delay is derived in closed-form. Simulation results validate that the theoretical delay matches the experimental data closely.