We study the propagation of premixed flames in two-dimensional channels accounting for heat-losses by conduction to the channel's walls and a prescribed Poiseuille flow. A diffusive-thermal model is used and the calculations reported are based on Arrhenius-type chemistry. Attention is focused on the influence of the magnitude of heat losses, the channel width, and the mean flow velocity. Special attention is devoted to the determination of the global burning rate and to extinction conditions. Depending on the channel width we discuss two possible modes of extinction: total flame extinction brought about in narrow channels by excessive losses, and partial flame extinction near the walls of wider channels. Our predictions of the quenching distance, namely the smallest channel's width that permits flame propagation, and the dead space in the case of partial extinction are in agreement with experimentally reported values. The sensitivity of the flame to an imposed flow, being directed either towards the fresh mixture or towards the burned gas, is examined with some details. Copyright © 2002 The Combustion Institute.