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Server replication is commonly used to improve the fault tolerance and response time of distributed services. An important problem when executing time-critical applications in a replicated environment is that of preventing timing failures by dynamically selecting the replicas that can satisfy a client's timing requirement, even when the quality of service is degraded due to replica failures and excess load on the server. We describe the approach we have used to solve this problem in AQuA, a CORBA-based middleware that transparently replicates objects across a local area network. The approach we use estimates a replica's response time distribution based on performance measurements regularly broadcast by the replica. An online model uses these measurements to predict the probability with which a replica can prevent a timing failure for a client. A selection algorithm then uses this prediction to choose a subset of replicas that can together meet the client's timing constraints with at least the probability requested by the client. We conclude with experimental results based on our implementation.