This paper deals with a simple but essential two-hop wireless relay network employing network coding and a slotted ALOHA protocol. Network coding is a recent and highly regarded technology for capacity enhancement on multiple unicast and multisource multicast networks. However, the performance of network coding on wireless relay networks employing random access protocols has not been analyzed. This paper provides closed-form expressions for the throughput and delay on two- hop wireless relay networks both with and without network coding from a theoretical perspective of the slotted ALOHA protocol. The analytical results are derived by solving queueing systems for the buffer activity at the relay node. The results show that the transmission probability of the relay node is a design parameter that is crucial to maximizing the achievable throughput of slotted ALOHA with network coding on a two- hop wireless relay network. Furthermore, this paper clarifies that the throughput is enhanced by controlling the transmission probability of the relay node such that it has considerable opportunity for network coding.