The conditions that lead to the extinction of a premixed flame propagating along a channel of height 2h(1) similar to delta(T) are studied using the thermo-diffusive approximation, with delta(T) = D-T/S-L, D-T and S-L representing, respectively, the thermal flame thickness, the thermal conductivity and the planar flame speed. It is found that flame propagation is greatly affected by conductive heat losses to the wall partial derivative T/partial derivative n = (b) over bar (T-T-0), where n denotes the transverse distance to the wall, T and T-0 are, respectively, the fluid's and wall's temperature and (b) over bar is the heat transfer parameter. The sensitivity of the flame to heat losses grows as the channel narrows, leading to complete flame extinction at extremely small values of (b) over bar = (b) over bar (c). As a way to overcome flame quenching at the walls, Lloyd and Weinberg [1] proposed the recirculation of part of the heat stored in the exhaust gases to preheat the cold combustible mixture. In order to understand the flame dynamics in the presence of heat recirculation, we analyze the problem of two parallel channels with a combustible mixture and an inert fluid moving in opposite directions, with maximum velocities m(1) and m(2) respectively, and where heat exchange is permitted through the common wall separating both channels. It is shown that flame extinction occurs if the velocity ratio m(2)/m(1) is outside the range m(2)/m(1) is an element of [m(21,min) m(21,max)], where the limiting values m(21,min) and m(21,max) are obtained numerically for a given set of parameters. The amplitude of this range depends, mainly, on the Damkholer number d = [h(1)/(D-T/S-L)](2), quantity that represents the ratio between the channel's height h(1) and the thermal flame thickness D-T/S-L. It is shown that heat recirculation is capable of extending combustion to very small h(1), but there is still a minimum value of the Damkholer number d(min) below which combustion is not possible. The evolution of d(min) is computed numerically to give values as small as d = 0.0025 for a given combination of the geometric parameters of the problem. The maximum flame temperature computed in the parallel channel configuration rises above the adiabatic flame temperature T-e due to the effect of the heat recirculation. This effect becomes more significant as d is reduced, leading to maximum temperatures close to T similar or equal to 1.4T(e) in very narrow channels. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.