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Abstract: In this paper the recurrent back-propagation and Newton algorithms for an important class of recurrent networks and their convergence properties are discussed. To ensure proper convergence behavior, recurrent connections must be suitably constrained during the learning process. Simulation results demonstrate that the algorithms with the suggested constraint have superior performance. 1. INTRODUCTION It is well known that feedforward neural networks may have difficulties in representing the sequential behavior of a target sequence and can perform only passive cognition. 4,13 This deficiency hampers the applications of feedforward networks in fields such as signal processing and dynamic control where temporal structure plays an important role. In contrast with feedforward networks, recurrent networks permit additional, internal feedback connections among units so that they are able to capture more dynamic characteristics and perform cognition even when inputs are static. This aspect o...