The use of renewable energy sources is a major concern nowadays, where efforts are made to achieve higher efficiencies. Among the different possibilities, Biogas production from organic waste represents an interesting technology. One difficulty arises as the system can be unstable under certain conditions, being able to systematically understand these conditions could lead to efficient control design. In this paper the stability analysis of an anaerobic biodigestor using the indirect Lyapunov's method is presented using the model (AM2).