Several directional MAC protocols for ad hoc networks using directional antennas have been proposed recently. Although directional antennas have great potential such as high spatial reuse and range extension, directional MAC protocols inherently introduce new problems arising from directivity. Deafness is one of the major problems and reduces the performance, caused by a lack of state information from neighbor nodes. This paper presents two directional MAC protocols, DMAC/DA (Directional MAC with Deafness Avoidance) and RI-DMAC (Receiver-Initiated Directional MAC), which handle the deafness problem, and mainly evaluates these protocols through extensive simulation study. DMAC/DA is a proactive handling method for deafness. In DMAC/DA, WTS (Wait To Send) frames are transmitted to notify the on-going communication to potential transmitters that may experience deafness. In this paper, DMAC/DA is enhanced by the next packet notification, called DMAC/DA with NPN, to distinguish transmitters from neighbors. On the other hand, RI-DMAC handles deafness reactively using a combination of sender-initiated and receiver-initiated operations. In RI-DMAC, each node polls a potential deafness node using RTR (Ready To Receive) after the completion of every dialog. The experimental results show that our proposed protocols outperform existing directional MAC protocols in terms of throughput, control overhead and packet drop ratio.