We propose to generalize TSK fuzzy model applying nonlinear functions in the rule consequences. We provide the model description and parameterization and discus the problem of model training and we recommend PSO for tuning parameters in membership functions and in nonlinear part of a rule consequence. We also propose some more or less formalized approach to nonlinear consequence selection and construction. Several examples demonstrate the main features of the proposed fuzzy models. The proposed approach reduces the average obtained model Root Mean Square Error (RMSE) with regard to the linear fuzzy model, as well that it allows to reduce the model complexity preserving the desired accuracy.