Recent research efforts in the fields of data stream processing and data stream management systems (DSMSs) show the increasing importance of processing data streams, e. g., in the e-science domain. Together with the advent of peer-to-peer (P2P) networks and grid computing, this leads to the necessity of developing new techniques for distributing and processing continuous queries over data streams in such networks. In this paper, we present a novel approach for optimizing the integration, distribution, and execution of newly registered continuous queries over data streams in grid-based P2P networks. We introduce Windowed XQuery (WXQuery), our XQuery-based subscription language for continuous queries over XML data streams supporting window-based operators. Concentrating on filtering and window-based aggregation, we present our stream sharing algorithms as well as experimental evaluation results from the astrophysics application domain to assess our approach.