Since occurrence of faults in different parts of a system as a complex abnormality is inevitable and could cause a total failure, Fault Detection and Accommodation (FDA) is finding ever widening attention for both industrial practitioners as well as academic researchers. In the large majority of real implementation of FDA, analytical model of the system, if known, may exert an impact on the performance of an FDA method. However, in some cases, such analytical model cannot be obtained in advance. Under unavailability assumption of the analytical model, in this paper we develop a data-driven method to identify and model three kinds of faults in nonlinear systems. Two Adaptive Neural-Fuzzy Inference Systems (ANFISs) are employed in this method, i.e.. the first one is used for building a model of the faultless plant using the historical data, and the second one for modeling the occurred faults. Parameters of the second ANFIS are adjusted in an indirect way based on minimization of difference between actual and model outputs. Simulation results for a nonlinear system are also presented to demonstrate the potentiality of the proposed method for fault identification.