This study is motivated by the observation that in combustion of hydrogen-oxygen/air and ethylene-oxygen mixtures the global activation energy appears to be high at low enough temperatures and low at high enough temperatures, reflecting the complex nature of the underlying chemistry. Stability analysis of a uniformly propagating planar premixed flame controlled by a stepwise ignition-temperature kinetics (representing the activation energy temperature-dependence) is carried out. It is shown that, for all its schematic nature, the diffusive-thermal model based on the ignition-temperature kinetics reproduces quite successfully the basic features of both cellular and pulsating instabilities typical of low and high Lewis number mixtures. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.