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Establishing an appropriate semantic overlay on peer-to-peer (P2P) networks to obtain both semantic ability and scalability is a challenge. Current DHT-based P2P networks are limited in their ability to support a semantic search. This paper proposes the distributed suffix tree (DST) overlay as the intermediate layer between the DHT overlay and the semantic overlay to support the search of a keyword sequence. Its time cost is sublinear with the length of the keyword sequence. Analysis and experiments show that the DST-based search is fast, load-balanced, and useful in realizing an accurate content search on P2P networks.