In this paper, we propose a time delay dynamic neural network (TDDNN) to track and predict a chaotic time series systems. The application of artificial neural networks to dynamical systems has been constrained by the non-dynamical nature of popular network architectures. Many of the drawbacks caused by the algebraic structures can be overcome with TDDNNs. TDDNNs have time delay elements in their states. This approach provides the natural properties of physical systems. The minimization of a quadratic performance index is considered for trajectory tracking applications. Gradient computations are presented based on adjoint sensitivity analysis. The computational complexity is significantly less than direct method, but it requires a backward integration capability. We used Levenberg-Marquardt parameter updating method. (c) 2006 Elsevier B.V. All rights reserved.