Abstract: A informational element (IE) is provided which permits the user to assign a precedence level to a call. A precedence/preemption connection admission control (P/P CAC) for use with any bandwidth allocation algorithm is also provided for processing a virtual circuit connection (VCC) request having an assigned precedence level, and for preempting one or more VCCs when a VCC request having a relatively higher precedence level is received at an ATM switch. Preferably, a resource allocator containing two databases, one listing all active virtual circuit connections and a second listing all preempted virtual circuits, is provided for storing the call parameters of preempted VCCs. According to a preferred embodiment, preempted VCCs may be reestablished. Reestablishment occurs according to various criteria. In addition, a second embodiment of a P/P CAC is provided in which active VCCs identified for preemption are buffered until the requested VCC is accepted by a downstream ATM switch.