The article presents real-time object detection and classification methods by unmanned aerial vehicles (UAVs) equipped with a synthetic aperture radar (SAR). Two algorithms have been extensively tested: classic image analysis and convolutional neural networks (YOLOv5). The research resulted in a new method that combines YOLOv5 with post-processing using classic image analysis. It is shown that the new system improves both the classification accuracy and the location of the identified object. The algorithms were implemented and tested on a mobile platform installed on a military-class UAV as the primary unit for online image analysis. The usage of objective low-computational complexity detection algorithms on SAR scans can reduce the size of the scans sent to the ground control station.