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This paper describes an attempt to apply a neural network method to forecast river flow rate following a fall of rain. The authors use a perceptron-type network comprised of three layers. The input data to the neural network are rainfall amounts and subsequent river flow rates. Further the predicted total volume and duration of the spell of rainfall in question are taken as additional input data. The output from the neural network is forecasted river flow rate. It is found from these investigations that the forecasting accuracy of the neural network is improved by utilization of the linear input-output relations of neurons.