  In the present work we study possible time dependent effects in Axion Dark
Matter searches employing resonant cavities. We find that the width of the
resonance, which depends on the axion mean square velocity in the local frame,
will show an annual variation due to the motion of the Earth around the sun
(modulation). Furthermore, if the experiments become directional, employing
suitable resonant cavities, one expects large asymmetries in the observed
widths relative to the sun's direction of motion. Due to the rotation of the
Earth around its axis, these asymmetries will manifest themselves as a diurnal
variation in the observed width.
