The stability of a continuous flow stirred tank reactor with two consecutive reactions A→B→C is studied with the direct method of Liapunov. Krasovskii`s method with the identity matrix is used to obtain a Liapunov function in the analysis of the system with single or multiple steady states. The results show that this method is mathematically conservative as expected. From the viewpoint of practical stability, however, this method predicts the regions of stability adequately.