This paper proposes a neural network (NN)-based adaptive control methodology to prevent congestion in high-speed asynchronous transfer mode (ATM) networks. The buffer dynamics at the switch is modeled as a nonlinear discrete-time system and a NN-based predictive controller is designed to predict the explicit values of the transmission rates of the sources so as to prevent congestion. Tuning methods are provided for the NN weights to estimate the unpredictable and statistically fluctuating network traffic. Mathematical analysis is given to demonstrate the stability of the closed-loop system so that a desired quality of service (QoS) can be guaranteed. The QoS is defined in terms of cell loss ratio (CLR) and latency. We derive design rules mathematically for selecting the NN tuning algorithm such that the desired performance is guaranteed during congestion and potential tradeoffs are shown. Simulation results are provided to justify the theoretical conclusions for single source/single switch scenario using ON/OFF data. Finally, comparison studies are also included to show the effectiveness of the proposed method over conventional rate-based and thresholding techniques during simulated congestion.