Generalized modeling principles of a nonlinear system with a dynamic fuzzy network (DFN)-a network with unconstrained connectivity and with dynamic fuzzy processing units called 'feurons', have been given. DFN model has been trained both in open loop and closed loop forms to satisfy these principles. Several system trajectories with a PRBS input have been used for open loop training. DFN model obtained from open loop training was used in an extended Kalman filter (EKF) in an observer design and with a PID controller design for a nonlinear system. For gradient computation adjoint sensitivity method has been used. (C) 2003 Elsevier Ltd. All rights reserved.