In this paper, we are concerned with the problem of furnishing an ATM-based B-ISDN with two bearer services supporting different grades of transfer quality. By so doing, we are able to improve the utilization of network resources and provide a higher degree of flexibility by not having to dimension the network to satisfy the most demanding traffic class. This is achieved by dynamically allocating network resources (bandwidth and buffers) using priority classes. The focus of this paper is on priority bandwidth and buffer management in the ATM communications nodes. We consider several different loss priority queueing strategies, differing in the degrees of resource sharing, namely complete sharing with pushout and head-of-the-line, partial buffer sharing, complete buffer partitioning but complete bandwidth sharing, and complete partitioning. A rather general multi-channel system model, the D([A1,A2])/D/c/B queue taking the possible correlation between the two traffic classes into account, is developed for performance evaluation of these schemes. We develop performance bounds (for any work-conserving discipline) and compare these schemes in terms of performance and implementation complexity. We find that several orders of magnitude improvement in the loss probability can be achieved for the high-priority class with little impact on the low-priority class performance.