A computationally efficient estimation technique is presented for a class of nonlinear systems consisting of memoryless nonlinearities combined with linear dynamic processes. The modeling approach is based on a useful sampled-data method for simulating such systems by adding a system state for each nonlinear element. The nonlinear estimator is next developed along the lines of the Kalman filter, but in contrast to the Extended Kalman Filter (EKF) the present approach does not require the linearization step after each recursive cycle. In addition, it also appears free from the well known divergence problems associated with the EKF. It is demonstrated that this new method is directly applicable to those feedback systems with both major nonlinearities, for example saturating gain blocks, and stochastic disturbances-- an example extremely difficult to handle with EKF techniques.