Call Admission Control (CAC) is one of the most fundamental preventive congestion control mechanisms in Asynchronous Transfer Mode (ATM) networks. Several mathematical approaches that have been proposed in the literature, which usually estimate the equivalent bandwidth that is required, achieve conservative approximations that result in reduced statistical gain and thus, in under-utilisation of the network resources. In this study, a new methodology is proposed which uses a Learning Automaton (LA) in combination with equivalent bandwidth approximations to reduce the percentage of overestimation. The learning algorithm that is used attempts to predict in real-time if a call-request should be accepted or not receiving as feedback a function of an estimate of the equivalent bandwidth. As will be shown, the proposed mechanism, whose hardware implementation is feasible, exhibits remarkable statistical gain compared with some classical CAC schemes of the literature and distinct improvement of the equivalent bandwidth approximations, Finally, some issues for extending this work are also discussed. (C) 2000 Elsevier Science B.V. All rights reserved.