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This paper considers two-hop wireless systems employing network coding and a carrier sense multiple access (CSMA) protocol. Network coding is a recent and highly regarded technology for the capacity enhancement of multiple unicast and multisource multicast networks. The two-hop wireless CSMA systems are often involved with the hidden node problem, but the impact of the hidden nodes on network coding has not been analyzed in theory. This paper provides explicit expressions of the throughput for single-relay two-hop wireless CSMA systems both without and with network coding. The throughput can be obtained from these expressions for given system parameters even when end nodes via the relay node are hidden each other. Furthermore it is shown that the transmit probability of the relay node is a design parameter that is crucial for maximizing the achievable throughput for CSMA systems with network coding. It is clarified that the throughput for CSMA systems can be enhanced as compared with that for slotted ALOHA systems in case of non-hidden end nodes whereas it deteriorates considerably in case of hidden end nodes.