This paper proposes a Time Delay Dynamic Fuzzy Network (TDDFN) that can be used for tracking and prediction of chaotic time series. TDDFN considered here has unconstrained connectivity and dynamical elements in its fuzzy processing units with time delay state feedbacks. The minimization of a quadratic performance index is considered for trajectory tracking applications. Gradient with respect to model parameters are calculated based on adjoint sensitivity analysis. The computational complexity is significantly less than direct method, but it requires a backward integration capability. For updating model parameters, Broyden-Fletcher-Golfarb-Shanno (BFGS) algorithm that is one of the approximate second order algorithms is used. The TDDFN network is able to predict the Mackey-Glass chaotic time series and gives good results for the nonlinear system identification.