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In this paper, we consider the neighbor discovery problem in wireless ad hoc networks with directional antennas. One key performance measure is how long it takes to discover all the neighbors given that nodes do not have priori knowledge where their neighbors are. One common impression is that algorithms using directional transmission/receive take longer time than those algorithms using omni-antennas. In this paper, we prove that this is not the case. Furthermore, most of the proposed algorithms are 1-way only, which is not suitable for networks with directional antennas. We first propose three 2-way random neighbor discovery algorithms (based on the algorithms in [Vasuden et al., 2005]), two of which may still use omni-antennas in certain stages of the algorithms and a new scan based algorithm. Then we derive analytical expressions for the average number of slots required to discover all the neighbors for the three 2-way random algorithms and for two scan based algorithms. Analytic and simulation results are presented to compare 4 of the algorithms. From the numerical results, we conclude that scan-based all-directional algorithms give the best performance among all the algorithms considered. If designed properly, all-directional algorithms can discover neighbors in less time than those algorithms using omni-directional antennas.