ATM switches have to provide traffic management functions to meet the QoS requirements of different service categories. Among the traffic management functions we will focus on connection admission control (CAC) and priority control in this paper. Besides the mechanisms and algorithms behind these functions the issue of application to a concrete architecture of an ATM multi-service workgroup switch is emphasized. For CAC a new method is proposed that is based on a simple approximation of the effective bandwidth. The difficulties occurring if connections with different parameters are mixed together are solved by handling CBR traffic separately and dividing the parameter space for VBR connections into several regions. Within the VBR regions the linear method is applied while for connections associated to different regions a reduced service rate is considered. The performance of both the priority control mechanisms and the CAC method is evaluated using analysis and simulation. Keywords AT...