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Streams are preferable over data stored in memory in contexts where data is too large or volatile, or a standard approach to data processing based on storing is too time or space consuming. Emerging applications such as publish-subscribe systems, data monitoring in sensor networks, financial and traffic monitoring, and routing of MPEG-7 call for querying streams. In many such applications, XML streams are arguably more appropriate than flat streams, for they convey (possibly unbounded) unranked ordered trees with labeled nodes. However, the flexibility enabled by XML streams in data modeling makes query evaluation different from traditional settings and challenging. This paper describes SPEX, a streamed and progressive evaluation of XML Path Language (XPath). SPEX compiles queries into networks of simple and independent transducers and processes XML streams with polynomial combined complexity. This makes SPEX especially suitable for implementation on devices with low memory and simple logic as used, for example, in mobile computing.