Nowadays, Unmanned Aerial Vehicles (UAVs) are widely applied in various domains, and collaborative UAVs are organized as Flying Adhoc Networks (FANETs) to deal with large tasks. However, there are lots of common anomalies in FANETs, such as Denial of Service (DoS) attacks, information disclosure, black hole attacks, and selfish behaviors. To detect these common anomalies with low overhead and maintain accuracy under the high probability of anomalies, we propose a Dual Detection System (DDS) by analyzing the impact of anomalies on messages. In the first detection phase, the Ground Station (GS) calculates average values based on the number of generated, relayed, received, and deleted messages, from statistics reported by all UAVs in FANETs. Then the GS compares each UAV’s statistics with average values to filter out suspicious UAVs. Considering that various abnormal statistics imply distinct anomalies in FANETs, in the second detection phase, one or more featured detections are implemented on suspicious UAVs, such as DoS attack detection, information disclosure detection, black hole attack detection, and selfish UAV detection. Afterwards, malicious or selfish UAVs are detected, and normal UAVs are forbidden to communicate with them. Finally, simulations are conducted on the Opportunistic Network Environment (ONE) simulator. Results show that the DDS can achieve superior detection performances over the state-of-the-art, even with the high probability of anomalies.