The problem of maintaining structured peer-to-peer (P2P) overlay networks in the presence of concurrent joins and failures of nodes is the subject of intensive research. The various algorithms underlying P2P systems are notoriously difficult to design and analyse. Thus, when verifying P2P algorithms, a real challenge is to find an adequate level of abstraction at which to model the algorithms and perform the verifications. In this paper, we propose an abstract model for structured P2P networks with ring topology. Our model is based on process algebra, which, with its well-developed theory, provides the right level of abstraction for the verification of many basic P2P algorithms. As a case study, we verify the correctness of the stabilization algorithm of Chord, one of the best-known P2P overlay networks. To show the correctness of the algorithm, we provide a specification and an implementation of the Chord system in process algebra and establish bisimulation equivalence between the two.