The extinction of premixed CH4/O-2/N-2 flames counterflowing against a jet of combustion products in chemical equilibrium was investigated numerically using detailed chemistry and transport mechanisms. Such a problem is of relevance to combustion systems with non-homogeneous air/fuel mixtures or recirculation of the burnt gases. Contrary to similar studies that were focused on heat loss/gain, depending on the degree of non-adiabaticity of the system, the emphasis here was on the yet unexplored role of the composition of counterflowing burnt gases in the extinction of lean-to-stoichiometric premixed flames. For a given temperature of the counterflowing products of combustion, it was found that the decrease of heat release with increase in strain rate could be either monotonic or non-monotonic, depending on the equivalence ratio partial derivative(h) of the flame feeding the hot combustion product stream. Two distinct extinction modes were observed: an abrupt one, when the hot counterflowing stream consists of either inert gas or equilibrium products of a stoichiometric premixed flame, and a smooth extinction, when there is an excess of oxidizing species in the combustion product stream. In the latter case four burning regimes can be distinguished as the strain rate is progressively increased while the heat release decreases smoothly: an adiabatic propagating flame regime, a non-adiabatic propagating flame regime, the so-called partially-extinguished flame regime, in which the location of the peak of heat release crosses the stagnation plane, and a frozen flow regime. The flame structure was analyzed in detail in the different burning regimes. Abrupt extinction was attributed to the quenching of the oxidation layer with the entire H-OH-O radical pool being comparably reduced. Under conditions of smooth extinction, the behavior is different and the concentration of the H radical decreases the most with increasing strain rate, whereas OH and O remain comparatively abundant in the oxidation layer. As the profile of the heat release rate thickens, the oxidation layer is quenched and the attack of the fuel relies more heavily on the OH radicals. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.