We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics have been studied extensively in the past, it is only in recent years that high-speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H-2 and O-2 that have been regarded as problematic in the literature-specifically, jumps in predicted concentrations, and inconsistencies between predictions and experiments have been reported for a radiolysis. We computationally map-out a critical concentration behavior for a radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H-2] and [O-2] where the H2O2 concentration is not unique-both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported a radiolysis data and that no such behavior should occur for ? radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for a radiolysis and could place more restrictive ranges on G-values from derived relationships between them.