A learning process system is provided for a neural network. The neural network is a layered network comprising an input layer, an intermediate layer and an output layer formed of basic units. In the basic units, a plurality of inputs is multiplied by a weight signal and the products are accumulated, thereby supplying the sum of products. An output signal is obtained using a threshold value function in response to the sum of products. An error signal is generated by an error circuit in response to a difference between the output signal obtained from the output layer and a teacher signal. A weight updating signal is determined in a weight learning circuit by obtaining a weight value in which the sum of the error values falls within an allowable range. Thus, the learning is performed in the layered neural network through use of a back propagation method. Through such learning in the layered neural network, an updating quantity to be obtained in the present weight updating cycle is determined in response to a once delayed weight updating quantity signal in a previous weight updating cycle and a twice delayed weight updating quantity obtained at a twice-previous weight updating cycle prior to the previous weight updating cycle.