Abstract The Ingard-Myers condition, modelling the effect of an impedance wall under a mean flow by assuming a vanishing boundary layer, is known to lead to an ll-posed problem in time-domain. By analysing the stability of a mean flow, uniform except for a linear boundary layer of thickness h, in the ncompressible limit, we show that the flow is absolutely unstable for h smaller than a critical hc and convectively unstable or stable otherwise. This critical hc is by nature independent of wave le ...