A novel learning algorithm for recurrent neurofuzzy networks is introduced in this paper. The core of the learning algorithm uses equality index as the performance measure to be optimized. Equality index is especially important because its properties reflect the fuzzy set-based structure of the neural network and nature of learning. Equality indexes are strongly tied with the properties of the fuzzy set theory and logic-based techniques. The neural network recurrent topology is built with fuzzy neuron units and performs neural processing consistent with fuzzy system methodology. Therefore neural processing and learning are fully embodied within fuzzy set theory. The performance recurrent neurofuzzy network is verified via examples of nonlinear systems modeling. Computational experiments show that the recurrent fuzzy neural models developed are simpler and that learning is faster than both, static neural and neural fuzzy networks and alternative recurrent fuzzy neural networks.1 155160Ku, C.C., Lee, K.L., Diagonal recurrent neural networks for dynamic systems control (1995) IEEE Trans. on Neural Networks, 6, pp. 144-156. , JanuaryWilliams, R.J., Zipser, D., A learning algorithm for continually running fully recurrent neural networks (1989) Neural Computation, (1), pp. 270-280Lee, C.H., Teng, C.C., Identification and control of dynamic systems using recurrent fuzzy neural networks (2000) IEEE Trans. on Fuzzy Systems, 8 (4), pp. 3493-366. , AugustBuckley, A., Hayashi, Y., Fuzzy neural networks: A survey (1994) Fuzzy Sets and Systems, 66, pp. 41-49Lin, C.T., Lee, C.S., (1996) Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems, , Prentice Hall, Upper Saddle River, N.JNürnberger, A., Radetzky, A., Kruse, R., Using recurrent neuro-fuzzy techniques for the identification and simulation of dynamic systems (2001) Neurocomputing, 36, pp. 123-147Nürnberger, A., A hierarchical recurrent neuro-fuzzy system (2001) Proc. of Joint 9th IFSA World Congress and 20th NAFIPS International Conference, pp. 1407-1412. , IEEEPedrycz, W., Neurocomputations in relational systems (1991) IEEE Trans. Pattern Analysis and Machine Intelligence, 13 (3), pp. 289-297. , MarchPedrycz, W., Gomide, F., (1998) An Introduction to Fuzzy Sets: Analysis and Design, , MIT Press, Cambridge, MACaminhas, W., Tavares, H., Gomide, F., Pedrycz, W., Fuzzy set based neural networks: Structure, learning and application (1999) Journal of Advanced Computational Intelligence, 3 (3), pp. 151-157Ballini, R., Scares, S., Gomide, F., A recurrent neurofuzzy network structure and learning procedure (2001) Proc. of the 10th IEEE International Conference on Fuzzy Systems - FUZZ-IEEE'2001, 3Pedrycz, W., Rocha, A., Fuzzy-set based models of neuron and knowledge-based networks (1998) IEEE Trans. on Fuzzy Systems, 4 (1), pp. 254-266Nozaki, K., Ishibuchi, H., Tanaka, H., Trainable fuzzy classification systems based on fuzzy if-then rules (1994) Proc. of the 3th IEEE International Conference on Fuzzy Systems, pp. 408-502Oliveira, M., Figueiredo, M., Gomide, F., A neurofuzzy approach for autonomous control (1994) Proc. of the 3th IEEE International Conference on Fuzzy Systems, Neural Nets and Soft Computing, pp. 597-598Rumelhart, D., Hinten, G.E., Williams, R.J., Learning representations by back-propagating errors (1986) Nature (London), 323, pp. 533-536Barto, A.G., Jordan, M.I., Gradient following without back-propagation in layered networks (1987) Proc. of the IEEE 1st International Conference on Neural Networks, 2, pp. 629-636. , San DiegoNarendra, K.S., Parthasarathy, K., Identification and control of dynamical systems using neural networks (1990) IEEE Trans. on Neural Networks, 1 (1)Wang, L.X., (1994) Adaptive Fuzzy Systems and Control, , Prentice-Hall