A time-dependent linearized approach is used to predict the amplification or the decay of an initial perturbation in the multistage axial compressor of high hub-to-tip ratio. This analysis shows that for unstalled flow regimes the change in perturbation amplitude remains limited. The linearized theory remains valid until the stall limit. It is shown that, near this limit, peripheral propagation of an induced perturbation takes place at an angular velocity close to one-half of rotor angular velocity. However in most cases this perturbation has a limited amplitude.