  We study in a strip of $\mathbb R^2$ a combustion model of flame propagation
with stepwise temperature kinetics and zero-order reaction, characterized by
two free interfaces, respectively the ignition and the trailing fronts. The
latter interface presents an additional difficulty because the non-degeneracy
condition is not met. We turn the system to a fully nonlinear problem which is
thoroughly investigated. When the width $\ell$ of the strip is sufficiently
large, we prove the existence of a critical value $Le_c$ of the Lewis number
$Le$, such that the one-dimensional, planar, solution is unstable for
$0<Le<Le_c$. Some numerical simulations confirm the analysis.
