This thesis considers a dynamic scheme for connection admission control (CAC) in asynchronous transfer mode (ATM) networks. ATM is known as the most promising transfer technique for B-ISDN which is considered to be a communication architecture capable of supporting multimedia services. CAC is commonly considered for deciding whether to accept or reject the connection at a call incoming stage to prevent traffic congestion, so that it is newly instituted in ATM networks for avoiding any congestion due to the high-speed transfer nature and the bursty characteristic of traffic streams. We propose a robust dynamic scheme for CAC which can increase network utilization at a guaranteed service quality. The scheme is modeled as M/M/s/N pure loss queueing system with customer in population leaving the system according to a Poisson process when the number of busy servers exceeds a certain threshold value. The queueing system parameters are derived from a source traffic model we assumed as a fluid-flow model. With the model, we may obtain a quality measure under the dynamic scheme. However an approximation model is tried with due to the explosively increasing computational dimension of the exact model. A simulation experiments are also made under more realistic situations to show the effectiveness of the proposed model.