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Mobile agents have attracted considerable interest in recent years. In the context of mobile agents, fault tolerance is crucial to enable the integration of mobile agent technology into today's business applications. This article identifies two important properties for fault-tolerant mobile agent execution: nonblocking and exactly-once. Nonblocking ensures that the agent execution can proceed despite a single failure of the agent or the machine, for instance. Replication is the generally adopted mechanism to prevent blocking, but may lead to multiple executions of the agent (i.e., a violation of the exactly-once property), which is undesirable with operations that have side effects. Hence, we propose that fault-tolerant mobile agent execution be modeled as a sequence of agreement problems. Our approach is nonblocking and ensures exactly-once execution. FATOMAS, our prototype fault-tolerant mobile agent system, implements our approach. Its performance evaluation illustrates the overhead of the replication mechanisms.