In this two-part paper, we describe a new congestion control scheme which employs an adaptive neural predictive technique to account for the control loop delays in the information transfer process in computer networks. In feedback-based congestion control schemes, large information transfer delays make the rate control signals received at the data sources or the network access points from the network outdated. The congestion control scheme described here employs a neural network to predict the state of congestion in a computer network over a prediction horizon. Based on the neural predictor output, source rate control signals are obtained by minimizing a cost function which represents the cumulative differences between a set-point and the predicted output. An analytical procedure for the source rate control signal computations is given using gradient functions of the neural network predictor.