Unmanned aerial vehicle (UAV)-aided two-way relaying networks are designed, where a UAV is deployed to assist multiple pairs of users in their information exchange. There are two basic approaches for the user pairs’ information exchange within a single time slot via the UAV relay. The first approach is based on full-duplex, where all participants operate in the full-duplex mode to transmit and receive signals simultaneously. However, all transceivers have to operate in the face of severe self-interference, which cannot be completely suppressed. The second approach is based on conventional half-duplex, where the users send their information to the UAV within a certain fraction of the time slot, and the UAV relays them within the remaining fraction to avoid the self-interference. In either approach, the joint bandwidth and power allocation maximizing the sum information exchange throughput under realistic resource and user throughput constraints poses a complex nonconvex problem. New inner approximations are proposed for developing path-following algorithms for their computation. Our numerical results show that the time-fraction-based half-duplex approach clearly outperforms the high-complexity full-duplex approach.