A simple first-principles model of counter current heat-recirculating combustors is developed, including the effects of heat transfer from the product gas stream to the reactant stream, heat loss to ambient, and heat conduction in the streamwise direction through the dividing wall (and heat transfer surface) between the reactant and product streams. It is shown that streamwise conduction through the wall has a major effect on the operating limits of the combustor, especially at small dimensionless mass fluxes (M) or Reynolds numbers that would be characteristic of microscale devices. In particular, if this conduction is neglected, there is no small-M extinction limit because smaller M leads to larger heat recirculation and longer residence times that overcome heat loss if M is sufficiently small. In contrast, even a small effect of conduction along this surface leads to significantly higher minimum M. Comparison is made with an alternative configuration of a flame stabilized at the exit of a tube, where heat recirculation occurs via conduction through tube wall; it is found that the counter-current exchanger configuration provides superior performance under similar operating conditions. Implications for microscale combustion are discussed. (C) 2003 The Combustion Institute. All rights reserved.