There are various traditional mathematical approaches used in ATM traffic control to maintain the QoS. However, most of these approaches are not suitable for handling the wide variety of ATM services and diversity of their combinations. The precise characteristics of the source traffic are not known and the service quality requirements change over time. Building an efficient network controller which can control the network traffic is a difficult task. The advantage of using NNs in ATM is that the QoS can be accurately estimated without detailed user action models or knowledge about the switching system architecture. The disadvantage is that it will take longer time to train with ATM network changes. In this paper, we use Genetic Algorithms in Neural Network weights training for ATM Call Admission Control (CAC) and Usage Parameter Control (UPC). The simulation results have shown not only a guarantee for the QoS of all the services, but also a saving of the system bandwidth and an improvement of the throughput.