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Several window constructs are usually specified in continuous queries over data streams as a means of limiting the amount of data processed each time and thus providing real-time responses. Current research has mostly focused on tackling the temporal volatility of the stream, overlooking other inherent features of incoming items. In this paper, we argue that novel window types, other than strictly temporal, can also prove adequate in providing finite portions of multidimensional streams. We systematically examine the particular case of spatiotemporal streams generated from moving point objects and we introduce a comprehensive classification of window variants useful in expressing the most common operations, such as range or nearest- neighbor search. Our investigation also demonstrates that composite windows, combining temporal and spatial properties, can effectively capture the evolving characteristics of trajectories and assist significantly in query specification.