Device-to-device (D2D) communication underlying cellular networks, allows direct transmission between two devices in each other's proximity that reuse the cellular resource blocks in an effort to increase the network capacity and spectrum efficiency. However, this imposes severe interference that degrades the system's performance. This problem may be circumvented by incorporating fractional frequency reuse (FFR) or soft frequency reuse (SFR) in OFDMA cellular networks. By carefully considering the downlink resource reuse of the D2D links, we propose beneficial frequency allocation schemes, when the macrocell has employed FFR or SFR as its frequency reuse technique. The performance of these schemes is quantified using both the analytical and simulation results for characterizing both the coverage probability and the capacity of D2D links under the proposed schemes that are benchmarked against the radical unity frequency reuse scheme. The impact of the D2D links on the coverage probability of macrocellular users (CUs) is also quantified, revealing that the CUs performance is only modestly affected under the proposed frequency allocation schemes. Finally, we provide insights concerning the power control design in order to strike a beneficial tradeoff between the energy consumption and the performance of D2D links. © 2016 IEEE.