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With the introduction of directional antennas in to the wireless ad hoc networks, there has been an intense work done on proposing a specialized MAC protocol that exploits the advantages of the directional antennas. Some protocols proposed extensions to the distributed coordination function (DCF) using directional antennas while other protocols proposed new MAC methods exploiting the directional transmission capability of directional antennas. MAC protocols proposed have exposed some new problems like hidden/exposed terminal problem and deafness that are specific to the directional antennas. Apart from the specific problems with directional antennas, mobility that is a general problem in the omnidirectional antennas is a specific problem which most of the protocols ignored, as it would reduce the efficiency of the proposed protocol using directional antennas. In this paper, we will exploit the mobility problem and discuss about the very few protocols that have considered the mobility in their models.