The paper is concerned with an extension of the classical relation between theflame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusivelystable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this studythe difficulty is resolved by incorporation of higher-order effects. As a result one ends up witha reduced model based on a coupled system of second-order dynamic equations for the flameinterface and its temperature. As an illustration the new model is applied for description ofdiffusively unstable stagnation-point flow flames.