This note investigates the stability of non-isothermal continuous homogeneous reaction systems involving S species, R reactions, p inlet streams, and one outlet stream. The analysis, which is based on Lyapunov's indirect method, is greatly simplified by transforming the reactor model of S+1 dynamic equations obtained from material and energy balances into R+1 dynamic equations expressed in terms of vessel extents of reaction and heat exchange. By linearizing this reduced model about the equilibrium point of interest, stability conditions can be established by computing the eigenvalues of a reduced system matrix. Furthermore, for the case of a single reaction of any order that obeys mass-action kinetics, novel sufficient stability conditions have been developed, which do not require computing eigenvalues. These stability conditions are proven to always hold for endothermic reactions using thermodynamical arguments. In addition, it is shown that the proposed stability conditions can be relaxed in the case of exothermic reactions depending on the value of heat-transfer coefficient. Two CSTR examples, with steady-state uniqueness and multiplicity behavior respectively, are used to illustrate the theoretical developments.