Distributed Denial of Service (DDoS) attacks remain a major threat in cybersecurity. Although extensive research has been conducted to detect and prevent DDoS attacks, industry still lacks effective tools and mechanism to achieve that goal. This is mainly due to the mutating (changing) nature of these attacks, as well as the development of new techniques used by the perpetrators of these acts. Traditional methods of dealing with DDoS attacks have proven to be deficient and inefficient in accurately detecting these attacks as most of those techniques were able to classify and detect only known classes of attacks. Therefore, successful identification of these attacks in their early stages is the utmost priority which is yet to be accomplished with all other detection techniques. This thesis addresses some of the challenges of detecting DDoS attacks on a real-time basis. A multifractal approach has been proposed for better and timely detection of DDoS attacks. The approach is based on measuring the complexity of the traffic self-affinity .The detection performance of this technique is compared with their traditional detection mechanisms, and an improvement in performance is reported in terms of time, computational speed, memory or resource usage and accuracy. The evaluation of the limitations of the traditional methods against multifractal approach is also considered. The use of multifractal analysis in detecting DDoS attacks provides an improvement compared to other techniques as a result of the multiscale complexity measures. Since this multiscale relationship exists in the Internet traffic of packets, anomalies can be detected on increasing time scales. This makes it possible to detect the presence of such attacks in the Internet traffic, an important feature that is missing in other current alternative detection techniques.