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Monitoring agents are deployed in distributed network environments to collect data and report events to a central coordinator. A widespread event is defined as an event that is observed by all monitoring agents simultaneously. Identifying widespread events can assist in detecting problems, such as cyberattacks, network malfunctions, and abnormal usages. However, detecting widespread events is challenging and a significant communication overhead can be incurred, because every monitoring agent must report any observed event to a central coordinator. In this paper, we study the problem of detecting widespread events accurately. Our proposed schemes can significantly reduce communication overhead and achieve perfect detection accuracy, which was not achieved by any previous studies. The new schemes can also identify generalized widespread events, defined as events observed by more than a predefined number of monitoring agents.