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The continuous sliding-window query model is used widely in data stream management systems where the focus of a continuous query is limited to a set of the most recent tuples. In this paper, we show that an interesting and important class of queries over data streams cannot be answered using the sliding-window query model. Thus, we introduce a new model for continuous window queries, termed the predicate-window query model that limits the focus of a continuous query to the stream tuples that qualify a certain predicate. Predicate-window queries have some distinguishing characteristics, e.g., (1) The window predicate can be defined over any attribute in the stream tuple (ordered or unordered). (2) Stream tuples qualify and disqualify the window predicate in an out-of-order manner. In this paper, we discuss the applicability of the predicate-window query model. We will show how the existing sliding-window query models fail to answer some of the predicate-window queries. Finally, we discuss the challenges in supporting the predicate-window query model in data stream management systems.