Recent advances in interference cancellation and signal processing techniques can enable full-duplex radios and multi-packet reception (MPR) capability, which will have significant impacts on the medium access control (MAC) design. In this paper, the authors study the MAC design in UAV ad-hoc networks with full-duplex radios and MPR. To efficiently handle the highly mobile environment of a UAV ad-hoc network, a token-based technique is used for updating information in the network. The MAC scheme in the presence of perfect and imperfect channel state information are formulated as a combinatorial optimization problem and a discrete stochastic optimization problem, respectively. Simulation results are presented to show the effectiveness of the proposed MAC.