A general formalism for the determination of stability criteria by the method of comparison functions is derived for nuclear reactors whose system dynamics are governed by a coupled set of space-dependent nonlinear differential equations. The results obtained are applicable to the nonlinear multigroup diffusion equations with temperature feedback. A stability criterion for the nontrivial equilibrium state is presented in a theorem. In addition, two corollaries are presented for the particular cases of negative feedback. The criteria so obtained represent a measure of the “dissipative” forces as estimated by the eigenvalues of the linearized problem vs a measure of the “disruptive” forces caused by the feedback. If the net effect is dissipative then the system is asymptotically stable in the sense of Lyapunov. Two examples are presented to illustrate the formalism and use of the criteria. In the second example, a stability criteria for two-group theory with linear temperature feedback is derived directly from the equations of motion by this method.