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We study the multicast throughput capacity for hybrid wireless mobile ad hoc networks (MANETs) with a directional antenna and delay constraint. The hybrid wireless network consists of a mobile ad hoc network with n nodes and m regularly placed base stations connected by high-bandwidth wired links. For the MANET, there are ns multicast sessions and each multicast session has one source which transmits identical informations to its associated p destinations. Assuming that the mobile nodes adopt 2D-i.i.d. mobility model, we investigate the ad hoc mode multicast throughput capacity when each node is equipped with a directional antenna along with a tolerant delay D. That is, a source node transmits to its p destinations only with the help of normal nodes within D consecutive time slots. Otherwise, the transmission will be switched to the infrastructure mode, where the base stations serve as relays. We find that the multicast throughput capacity of a hybrid wireless MANETs greatly depends on the delay constraints D, the number of base stations m, and the beamwidth of directional antenna theta. We show that the multicast throughput capacity of the hybrid directional wireless network is Θ(√θ) + Θ(m/nsp W2) bits/sec, if Ω(ns/(log p)2(log(θnsp))2); Θ(m/nsp W2) bits/sec, if D = O(3√(ns/(log p)2(log(θnsp)))2); and O((log p)(log(θnsp))√(θD/ns)) + Θ(m/nsp W2) bits/sec, otherwise. We analyze the impact of D, m and θ on the multicast throughput capacity of the hybrid MANET. Finally, we derive lower bound of the muticast throughput using a similar raptor coding approach as in.