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We introduce an extension of the XQuery language, Flux, that supports event-based query processing and the conscious handling of main memory buffers. Purely event-based queries of this language can be executed on streaming XML data in a very direct way. We then develop an algorithm that allows to efficiently rewrite XQueries into the event-based FluX language. This algorithm uses order constraints from a DTD to schedule event handlers and to thus minimize the amount of buffering required for evaluating a query. We discuss the various technical aspects of query optimization and query evaluation within our framework. This is complemented with an experimental evaluation of our approach.