In this paper, an online system identification method is introduced for lifetime diagnostic of supercapacitors. The online strategy uses a Lyapunov-based adaptation law to estimate online the supercapacitor's parameters. Therefore, the adaptive observer's stability is guaranteed by Lyapunov's direct method. State-of-health (SoH) estimation is crucial since aging introduces degradation in supercapacitors' performance, which might eventually lead to their failure. SoH is usually measured by offline time or frequency domain characterization techniques such as spectroscopy. However, these methods require interruption of the system's operation, and hence, they are not suitable for real-time applications such as electric vehicles. Unlike other online estimation strategies, only voltage and current measurements are required. Simulation and experimental results along with comparison against two different methods highlight the effectiveness of the proposed approach in estimating the SoH.