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In data stream systems, data does not appear in form of persistent relations, but rather arrives in multiple, continuous, rapid, time-varying streams. Although, the nature of data streams is on-line, the well-known data stream models don't consider on-line query processing. This is a major deficit in these environments. In this paper an on-line query processing model for data streams is presented in which finite state automata is used. Architecture of the proposed query processing model, structure of the finite state automata, and relevant algorithms for on-line data stream query processing are presented. It is tested using an on-line auction environment and its performance in term of response time, tuple latency, number of operations and required memory space is evaluated and compared with the existing system via simulation.