A theoretical study about the autoignition phenomenon has been performed in this article. The hypotheses of the Livengood & Wu integral have been revised, concluding that the critical concentration of chain carriers is not constant. However, its validity under engine conditions has been justified. Expressions to characterize the temporal evolution of the concentration of chain carriers, as well as the critical concentration of active radicals and the ignition delay, have been obtained starting from the Glassman's model. A new expression to predict ignition delays under variable conditions has been developed and the results obtained with this expression have been compared with those obtained from the Livengood & Wu integral. Two different fuels have been studied: isooctane (as a gasoline surrogate) and n-heptane (as a diesel fuel surrogate). The new method to predict ignition delays under variable conditions has shown, in general, better results than the classic Livengood & Wu integral, but the inability of the Glassman's model to reproduce the negative temperature coefficient regime should be improved in future works. (C) 2015 Elsevier Ltd. All rights reserved.