SUMMARYFour classes of traffic are present in a bank communication system: Alarm, BSC, SNA and IP traffic, with each class of traffic having different priority requirements. In this paper, a prioritized multiple access protocol is introduced which is capable of handling the above priority classes. The proposed protocol makes use of learning automata in order to dynamically assign the available bandwidth to the priority classes. In this way, it is capable of being adapted to the traffic conditions. The proposed protocol, is applicable to a broad range of prioritized LANs, as it can be easily extended to support multiple classes of traffic.