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In this paper, we formulate a joint optimization problem for resource allocation and scheduling in full-duplex multiple-input multiple-output orthogonal frequency division multiple access (MIMO-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 and non-delay sensitive users. We also consider a theoretically optimal hybrid relaying scheme as a performance benchmark, which allows a dynamic selection between AF relaying and DF relaying protocols with full-duplex and half-duplex relays. We show that under some mild conditions the optimal transmitter precoding and receiver post-processing matrices jointly diagonalize the MIMO-OFDMA relay channels for all considered relaying protocols transforming the resource allocation and scheduling problem into a scalar optimization problem. Dual decomposition is employed to solve this optimization problem and a distributed iterative resource allocation and scheduling algorithm with closed-form power and subcarrier allocation is derived. Simulation results not only illustrate that the proposed distributed algorithm converges to the optimal solution in a small number of iterations, but also demonstrate the potential performance gains achievable with full-duplex relaying protocols.