Ignition and extinction of steady state combustion are known to be associated with the lower and upper turning points on the "S"-curves. In the present study, this concept is further investigated with eigen-analysis on the Jacobian matrix for oxidation of methane and dimethyl ether (DME), respectively, in perfectly stirred reactors (PSRs). It was found that there can be multiple ignition and extinction turning points on the "S"-curves for DME-air due to negative temperature coefficient (NTC) behaviors. Furthermore, the physical extinction points for DME-air obtained from flame stability analysis can be different from the turning points on the "S"-curves although there is no differential diffusion or heat loss in PSR. Physically unstable segments were observed on the branches of an "S"-curve for DME-air corresponding to both strong and cool flames. A rigorous definition of ignition and extinction of steady state combustion based on eigen-analysis of the Jacobian matrix is proposed for practical fuels in the present study. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.