It might be more efficient that detections of distributed denial of service (DDoS) attacks are done in backbone domain than in individual local networks or links. However, because existing schemes for detecting DDoS attack symptoms have been focused on individual packets or flows, they require much higher computational complexities. In this paper, we propose an efficient method to detect DDoS attack symptoms in backbone networks. Unlike conventional schemes focused on individual packets or flows, the proposed method is carried at aggregate traffic level. So, our proposed schemes can be operated with very lower computational complexity, and can be run in very high-speed backbone networks.