The first and second Lyapunov methods were adapted to analyze the stability of a tubular chemical reactor with recycle. The criterion of local stability in the form of inequalities was derived using Lyapunov's first method. It is an explicit algebraic form, despite the fact that the mathematical model of the reactor is a partial differential problem with a boundary condition. As part of the second Lyapunov method, a mathematical criterion for non-local stability was derived in the form of an increase of Lyapunov's function. Both criteria are presented on graphs.