A mutually anonymous service hides the identity of a client from the service provider and vice-versa. Providing mutual anonymity usually requires a large number of participants. While peer-to-peer (P2P) networks are capable of recruiting a large number of participants, reliable anonymous communication in these architectures, with low bandwidth usage, still needs further investigation. This paper presents MuON, a protocol to achieve mutual anonymity in unstructured P2P networks. MuON leverages epidemic-style data dissemination to deal with the high churn (changes in system membership) characteristic of unstructured P2P networks. The results from our security analysis and simulation show that MuON provides mutual anonymity over unstructured P2P networks while maintaining predictable latencies, high reliability, and low communication overhead