Computation was first performed for the first-stage ignition delay, τ1, in the homogeneous autoignition of n-heptane/air mixtures. Results show that τ1 possesses a minimum value, τ1,min, in that it first decreases and then increases with increasing temperature, and that τ1 is largely insensitive to the equivalence ratio (ρ) and pressure (p) of the mixture when the temperature is sufficiently below the initial temperature corresponding to τ1,min. This is consistent with the experimental results from shock tubes and rapid compression machines. Furthermore, in this regime the global reaction order was found to be close to unity, hence supporting the notion that the limiting steps in this temperature regime are the RH2 isomerization reactions, which in turn explains the insensitivity of τ1 on ρ and p. However, when the temperature approaches that of τ1,min, competition of the β scission reactions of the alkyl radicals with the lowtemperature chemistry chain reactions as well as the equilibrium shift of the oxygen combination reactions increases the first-stage ignition delay and consequently results in τ1,min. The corresponding global reaction order also increases, to about two, indicating the progressive importance of the oxygen combination reactions. Additional simulation of ignition in the nonpremixed counterflow showed that the characteristic time scale given by the critical strain rate, hence the reaction order, also follows the same density (pressure) dependence as those for τ1 and τ1,min, indicating the preservation and thereby essential role of the NTC-chemistry in transport-affected ignition.