In this paper a new method of neural filtering using artificial neural network systems is presented for the filtering problems of linear and nonlinear, stationary and nonstationary stochastic signals. The neural filter (denoted neurofilter) developed in this paper has either finite impulse response (FIR) structure or infinite impulse response (IIR) structure. The neurofilter differs from the conventional linear digital FIR and IIR filters because the artificial neural network system used in the neurofilter has a nonlinear structure due to the sigmoid function. Numerical studies for the estimation of a second-order Butterworth process are performed by changing the structures of the neurofilter in order to evaluate the performance indices under changes of the output noises or disturbances. The results obtained from these studies verified the capabilities which are essentially necessary for on-line filtering of various stochastic signals.