—By enabling two adjacent mobile devices to establish a direct link, device-to-device (D2D) communication can increase the system throughput over underlaying wireless networks, where D2D and cellular communications coexist to share the same radio resource. Traditional D2D schemes mainly focus on maximizing the system throughput without taking into account the quality-ofservice (QoS) provisioning. To overcome this problem, we develop a framework to investigate the impact of delay-QoS requirement on the performance of D2D and cellular communications in underlaying wireless networks. Then, we propose the optimal power allocation schemes with statistical QoS provisioning for the following two channel modes: 1). co-channel mode based underlaying wireless networks where D2D devices and cellular devices share the same frequency-time resource; 2). orthogonalchannel mode based underlaying wireless networks where the frequency-time resource is partitioned into two parts for D2D devices and cel...