Consider a text filtering server that monitors a stream of incoming documents for a set of users, who register their interests in the form of continuous text search queries. The task of the server is to constantly maintain for each query a ranked result list, comprising the recent documents (drawn from a sliding window) with the highest similarity to the query. Such a system underlies many text monitoring applications that need to cope with heavy document traffic, such as news and email monitoring.In this paper, we propose the first solution for processing continuous text queries efficiently. Our objective is to support a large number of user queries while sustaining high document arrival rates. Our solution indexes the streamed documents in main memory with a structure based on the principles of the inverted file, and processes document arrival and expiration events with an incremental threshold-based method. We distinguish between two versions of the monitoring algorithm, an eager and a lazy one, which differ in how aggressively they manage the thresholds on the inverted index. Using benchmark queries over a stream of real documents, we experimentally verify the efficiency of our methodology; both its versions are at least an order of magnitude faster than a competitor constructed from existing techniques, with lazy being the best approach overall.