The first-stage ignition delay of n-heptane/air mixtures is computationally studied using detailed mechanism and theoretically studied using eigenvalue analysis of simplified systems. Results show that the delay has a turnover behavior as temperature increases, being dominated by the competition of low temperature branching and termination channels as well as the competition of forward and reverse reaction channels. As temperature increases to the intermediate range, the termination and reverse pathways result in a minimum in the delay, the state of which is theoretically derived. Simple analytical solutions for the delay as well as the species evolutions are presented to identify the rate constants that control the first-stage ignition and quantify the influence of the mixture composition, initial temperature and system pressure. It is further demonstrated that the above results also hold for n-octane/air and iso-octane/air mixtures. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.