Peer-to-peer systems, exchanging dynamic documents through Web services, are a simple and effective platform for data integration on the internet. Dynamic documents can contain both data and references to external sources in the form of links, calls to web services, or coordination scripts. XML standards, and industrial platforms for web services, provide the technological basis for building such systems, and process algebras are a promising tool for studying and understanding their formal properties. Core Xdπ is the explicitly located version of Xdπ, a process calculus designed for reasoning about dynamic Web data, based on explicit repositories of higher-order semistructured data and π-calculus-like processes which can communicate with each other, query and update the local repository, or migrate to other peers to continue execution. We study behavioural equivalences for Core Xdπ processes. To help with the proofs, which require a costly property of closure under contexts, we d...