In the context of an IP-over-ATM access and transport network, carrying guaranteed quality (CBR, rt-VBR) services as well as IP datagrams (as ABR or UBR traffic classes), we consider the joint problems of Call Admission Control (CAC), bandwidth allocation and routing. The presence of distributed access multiplexers is assumed, which are both geographically dispersed (e.g., at the user premises) and hierarchically structured. Such multiplexers are intelligent devices with decision making capabilities that operate jointly, in order to make the best possible use of the transport capacity of the access network and to maintain the Quality of Service (QoS) requirements of different users and service classes. Following the physical system organization, a hierarchical control structure is defined, where the admission of calls for real-time traffic classes (or different users) is performed by independent controllers; the latter are parametrized by the bandwidths allocated by a common link agent, playing the role of a “link coordinator” in the hierarchical control scheme. This decision maker aims at minimizing a general cost that captures QoS requirements both at the call-level (call blocking probability) for QoS-aware, connection-oriented services and at the cell-level (cell loss probability) for connectionless, best-effort, ones. The control architecture also reflects the multilayer hierarchy introduced by the presence of multiple teletraffic time scales, by essentially decoupling the above problem from that of ensuring QoS at the cell-level for services of the first type. We derive the optimal parameters’ setting from the numerical solution of a mathematical programming problem. Then, the same structure is applied to link multiplexers of the transport network nodes, which are supposed to possess both ATM and IP switching/routing capabilities. Routing strategies at both ATM and IP levels are defined, which are combined with the above described CAC and bandwidth allocation scheme. The performance of the whole structure is tested by simulation.