This project will address the fundamental issues of robustness and adaptiveness in the identification of dynamic systems in both series-parallel and parallel formulations. These two issues have been the topics of major concentrated research activities in system identification, control and filtering in the past 20 years. generally speaking, a system identifier should be adaptive to adaptation-worthy environmental parameters and robust to these which are adptative-unworthy. Taking a synthetic approach inspired by the development of the artificial neural networks (ANNs) it will lay the mathematical foundations, develop the methodologies, and test their feasibility's for robust and/or adaptive identification of dynamic systems in the project. The main idea for adaptive identification is to use the nonlinear and linear weights of an adaptive neural identifier as the long and short-term memory respectively, the former being determined in a prior off-line training and the latter adjusted on-line by an LMS or RLS algorithm. Such an adaptive neural identifier is expected to have the advantages of minimizing computation, focusing on learning about and adapting to the adaptation-worthy environmental parameters, and eliminating poor local extreme of the performance surface during the operation of the adaptive neural identifier. This idea was inspired by the way a brain performs adaptation.