In Kim et al. [(1997) A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems. Automatica 33(8), 1539-1543], authors present an excellent neural network (NN) observer for a class of nonlinear systems. However, the output error equation in their paper is strictly positive real (SPR) which is restrictive assumption for nonlinear systems. In this note, by introducing a vector b(0) and Lyapunov equation, the observer design is obtained without requiring the SPR condition. Thus, our observer can be applied to a wider class of systems. (c) 2005 Elsevier Ltd. All rights reserved.