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Wireless sensor networks can be used for event warning applications. Till date, in most of the proposed schemes, the raw or aggregated sensed data are periodically sent to a data consuming center. However, with those schemes, the occurrence of an emergency event such as a fire is hardly reported timely, which is a strict requirement for event warning applications. In wireless sensor networks, it is also highly desired to conserve energy so that network lifetime can be maximized. Furthermore, to ensure the quality of surveillance, some applications require that if an event occurs, it needs to be detected by at least k sensors, where k is a user-defined parameter. In this work, we examine the Timely Energy-efficient k-Watching Event Monitoring (TEKWEM) problem and propose a scheme, which involves an event detection model and a warning delivery model, for monitoring composite events and delivering warnings to users. Theoretical analysis and simulation results are shown to validate the proposed scheme.