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In this paper, a recurrent compensatory neuro-fuzzy system (RCNFS) is proposed for identification and prediction. The compensatory-based fuzzy reasoning method is using adaptive fuzzy operations of neuro-fuzzy systems that can make the fuzzy logic systems more adaptive and effective. The recurrent network is embedded in the RCNFS by adding feedback connections in the second layer, where the feedback units act as memory elements. Also, an online learning algorithm is proposed to automatically construct the RCNFS. They are created and adapted as online learning proceeds via simultaneous structure and parameter learning. Finally, the RCNFS is applied in several simulations. The simulation results of the dynamic system modeling have shown that 1) the RCNFS model converges quickly; 2) the RCNFS model requires a small number of tuning parameters; 3) the RCNFS model can solve the temporal problems and approximate a dynamic system.