In this paper, we formulate a joint optimization problem for resource allocation and scheduling in full-duplex orthogonal frequency division multiple access (OFDMA) relaying systems with amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Our problem formulation takes into account heterogeneous data rate requirements for delay sensitive users. Besides, a theoretically optimal hybrid relaying, which allows a dynamic selection between AF relaying and DF relaying protocols with full-duplex relays or half-duplex relays, is also considered in the problem formulation and serves as a performance benchmark. A dual decomposition method is employed to solve the resulting optimization problem and a novel distributed iterative resource allocation and scheduling algorithm with closed-form power and subcarrier allocation is derived. Simulation results illustrate that the proposed distributed algorithm requires only a small number of iterations to achieves practically the same performance as the optimal centralized algorithm.