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One of the Next Generation Internet (NGI) objectives is to offer services supported by large bandwidth connectivity, such as multimedia services. However their Quality of Service (QoS) is strongly influenced also by resilience. This paper focuses on the important problem of server selection with the highest two-terminal availability for distributed multimedia services. An analytical model gives optimal global server selection in terms of the highest two-terminal reliability for client-server connection in simple networks. For more complex networks a heuristic algorithm is utilized. The proposed algorithm allows to obtain better reliability values than the common shortest path server selection scheme.