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We investigate the possibility of using directional antennas for medium access control in wireless ad hoc networks. Previous research in ad hoc networks typically assumes the use of omnidirectional antennas at all nodes. With omnidirectional antennas, while two nodes are communicating using a given channel, MAC protocols such as IEEE 802.11 require all other nodes in the vicinity to remain silent. With directional antennas, two pairs of nodes located in each other's vicinity may potentially communicate simultaneously, increasing spatial reuse of the wireless channel. Range extension due to higher gain of directional antennas can also be useful in discovering fewer hop routes. However, new problems arise when using directional beams that simple modifications to 802.11 may not be able to mitigate. This paper identifies these problems and evaluates the tradeoffs associated with them. We also design a directional MAC protocol (MMAC) that uses multihop RTSs to establish links between distant nodes and then transmits CTS, DATA, and ACK over a single hop. While MMAC does not address all the problems identified with directional communication, it is an attempt to exploit the primary benefits of beamforming in the presence of some of these problems. Results show that MMAC can perform better than IEEE 802.11, although we find that the performance is dependent on the topology and flow patterns in the system.