Autonomous unmanned aerial systems (UAS) are having an increasing impact in the scientific community. One of the most challenging problems in this research area is the design of robust real-time obstacle detection and avoidance systems. In the automotive field, applications of obstacle detection systems combining radar and vision sensors are common and widely documented. However, these technologies are not currently employed in the UAS field due to the major complexity of the flight scenario, especially in urban environments. In this paper, a real-time obstacle-detection system based on the use of a 77 GHz radar and a stereoscopic camera is proposed for use in small UASs. The resulting system is capable of detecting obstacles in a broad spectrum of environmental conditions. In particular, the vision system guarantees a high resolution for short distances, while the radar has a lower resolution but can cover greater distances, being insensitive to poor lighting conditions. The developed hardware and software architecture and the related obstacle-detection algorithm are illustrated within the European project AURORA. Experimental results carried out employing a small UAS show the effectiveness of the obstacle detection system and of a simple avoidance strategy during several autonomous missions on a test site.