Abstract-Full duplex (FD) communications has the potential to double the capacity of a half duplex (HD) system at the link level. However, in a cellular network, FD operation is not a straightforward extension of half duplex operations. The increased interference due to a large number of simultaneous transmissions in FD operation and realtime traffic conditions limits the capacity improvement. Realizing the potential of FD requires careful coordination of resource allocation among the cells as well as within the cell. In this paper, we propose a distributed resource allocation, i.e., joint user selection and power allocation for a FD multi-cell system, assuming FD base stations (BSs) and HD user equipment (UEs). Due to the complexity of finding the globally optimum solution, a sub-optimal solution for UE selection, and a novel geometric programming based solution for power allocation, are proposed. The proposed distributed approach converges quickly and performs almost as well as a centralized solution, but with much lower signaling overhead. It provides a hybrid scheduling policy which allows FD operations whenever it is advantageous, but otherwise defaults to HD operation. We focus on small cell systems because they are more suitable for FD operation, given practical self-interference cancellation limits. With practical self-interference cancellation, it is shown that the proposed hybrid FD system achieves nearly two times throughput improvement for an indoor multi-cell scenario, and about 65% improvement for an outdoor multi-cell scenario compared to the HD system.