Two multilayer recurrent neural networks are presented for on-line synthesis of asymptotic state estimators for linear dynamical systems. The first recurrent neural network is composed of two layers to compute output gain matrices with desired poles. The second recurrent neural network is composed of four layers to compute output gain matrices with desired poles and minimal norm. The proposed multilayer recurrent neural networks are shown to be capable of synthesizing asymptotic slate estimators for linear dynamic systems in real time. The operating characteristics of the recurrent neural networks for state estimation are demonstrated by three illustrative examples.