In the present work we study possible signatures in the Axion Dark Matter searches. We focus on the dependence of the expected width in resonant cavities for various popular halo models, leading to standard velocity distributions, e.g. Maxwell-Boltzmann, as well as phase-mixed and non-virialized axionic dark matter (flows, caustic rings). We study, in particular, the time dependence of the resonance width (modulation) arising from such models. We find that the difference between the maximum (in June) and the minimum (in December) can vary by about 10% in the case of standard halos. In the case of mixed phase halos the variation is a bit bigger and for caustic rings the maximum is expected to occur a bit later. Experimentally such a modulation is observable with present technology. (C) 2016 The Authors. Published by Elsevier B.V.