Two-dimensional symmetric and non-symmetric premixed flames propagating in a narrow channel subject to a Poiseuille flow are investigated within the context of a diffusive-thermal model. Attention is focussed on the impact of the flame-wall heat exchange on the structure and stability of flames. It is found that an increase in the heat-losses leads to a discontinuity of the steady-state response curves: for Le < 1 the flame extinguishes inside a finite interval of flow rate values while for Le > 1 the flame cannot exist for flow rates larger or smaller than some critical values. Linear stability analysis of two-dimensional steady-state flames is also performed. It is shown that for symmetric flames with low Lewis number the heat-losses produce a stabilization effect while for flames with high Lewis number the increase in heat-losses tends to flame destabilization, producing oscillatory (symmetric or non-symmetric) behavior. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.