Kinetic modeling of the low-temperature (typically T ≤ 200 • C) thermal aging of polymers is a problem of great technological importance, owing to the continuously increasing needs of industry in terms of reliable methods for lifetime prediction. In the temperature domain under consideration, for most hydrocarbon substrates, oxidation proceeds by a radical chain reaction initiated by bimolecular hydroperoxide decomposition. In other words, the reaction generates its own initiator, which explains its strong autoaccelerated character. The most pertinent model is, to our opinion, the model elaborated by Tobolsky et al. (J Am Chem Soc 1950, 72, 1942 in the early 1950s. This model is, however, based on three questionable assumptions: the existence of a stationary state for radical concentrations (hypothesis S), the presence of oxygen in excess (hypothesis E), and the fact that the onset of steady state can be observed in the domain of low conversions, where the substrate consumption can be neglected (hypothesis L). One hypothesis (S) lacks consistency. A sounder alternative, which does not modify significantly the mathematical expressions of the model, will be proposed. The other hypotheses (E and L) can be justified in certain cases, but the limits of their domain of validity were never established to our knowledge. It is tried, here, to express these limits in function of fundamental parameters: rate constants and concentrations of reactants. C 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 666