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In this paper, we investigate the benefits of applying a form of network coding known as random linear coding (RLC) to unicast applications in disruption-tolerant networks (DTNs). Under RLC, nodes store and forward random linear combinations of packets as they encounter each other. For the case of a single group of packets originating from the same source and destined for the same destination, we prove a lower bound on the probability that the RLC scheme achieves the minimum time to deliver the group of packets. Although RLC significantly reduces group delivery delays, it fares worse in terms of average packet delivery delay and network transmissions. When replication control is employed, RLC schemes reduce group delivery delays without increasing the number of transmissions. In general, the benefits achieved by RLC are more significant under stringent resource (bandwidth and buffer) constraints, limited signaling, highly dynamic networks, and when applied to packets in the same flow. For more practical settings with multiple continuous flows in the network, we show the importance of deploying RLC schemes with a carefully tuned replication control in order to achieve reduction in average delay, which is observed to be as large as 20% when buffer space is constrained.