A new theoretical basis is presented for the practically important problem of predicting ignition delays in systems undergoing spontaneous combustion. An approximate lower bound for the ignition delay is derived in the universally applicable form τi = ua 2 e1 ua (1 - e- Δ / ua 2 ), where the dimensionless term represent ignition delay time, ti, ambient temperature, ua, and a defined temperature excess within the reactants, Δ. The predictions err on the side of safety. The application pertain to temperature ranges above criticality that are of practical importance, but the extent to which the ambient temperature exceeds that at criticality, which is extremely difficult to obtain accurately in marginally supercritical conditions, is not required. The prediction of the (long) ignition delays associated with large amounts of material under supercritical conditions during processing, storage or transport, from measured times to ignition of laboratory-scale samples, by used of the approximate theory, is also discussed. The size of the system is taken into account in a natural way be the choice of ua (in supercritical conditions) at which the prediction of ti is to be made. Comparisons are made between the ignition delay times and their temperature dependence that are predicted from the approxima theory, calculated from numerical simulations of ignition in a system in which heat transport occurs by thermal conduction, and measured in laboratory-scales experimental studies of ignition in a finely divided, particulate solid. The experimental results are also used to show how ignition delays in large amounts of material being stored or processed at different temperatures may be obtained in a practical case.