The role of connection admission control (CAC) for an asynchronous transfer mode (ATM) switch is to determine, given a set of signaled traffic descriptors and requested quality of service (QoS) contracts, whether a new connection should be accepted or rejected. CAC bases the decision to accept a new connection on the current state of the switch, which must be able to meet the requested QoS of the new connection and maintain the QoS commitments to existing connections. In addition, CAC must appropriately allocate and reallocate resources as connections are established and released. In this paper, we present the design of the CAC function for the GlobeView®-2000 ATM core switch (ACS). This design integrates the best of the existing CAC theories for different ATM service classes into a unified, efficient framework that strives for both a high system utilization and a high call processing rate. The main features we describe include an effective bandwidth algorithm for constant-bit-rate (CBR) connections, a unified admission control for real-time and non-real-time variable-bit-rate (rt-VBR and nrt-VBR) connections, an approximation method for the nonlinear admission boundary of the VBR service class, and resource sharing schemes for both buffer allocation in the shared-memory fabric (SMF) and bandwidth sharing at output links.