This paper describes the architecture and training procedure of a recurrent fuzzy system ( RFS). The RFS is composed of a fuzzy inference system ( FIS) and a delayed feedback connection. The recurrent property comes from feeding the FIS output back to the FIS input via an adjustable feedback parameter. Both the on- line and off- line training procedures based on the backpropagation- through- time ( BPTT) algorithm have been investigated. The adjoint model of the RFS is obtained and used to compute the gradients. It is shown that the off- line training is insufficient to adapt to changes in system dynamics. So, an on- line training procedure is derived. In this procedure, a first in first out stack is used to store a certain history of the input - output data to perform a truncated BPTTalgorithm. A quasi- Newton optimization method with a line search algorithm is used to adjust the RFS parameters. The performance of the developed RFS is demonstrated by applying to the identification of nonlinear dynamic systems. The simulation studies show that the proposed identification model has the ability to learn dynamics of highly nonlinear systems and compensate system uncertainties. The results are promising for the further application in the area of control and modeling. (c) 2006 Elsevier B. V. All rights reserved.