Fault-tolerant real-time systems are typically based on active replication where replicated entities are required to deliver their outputs in an identical order within a given time interval. Distributed scheduling of replicated tasks, however, violates this requirement if on-line scheduling, preemptive scheduling, or scheduling of dissimilar replicated task sets is employed. This problem of inconsistent task outputs has been solved previously by coordinating the decisions of the local schedulers such that replicated tasks are executed in an identical order. Global coordination results either in an extremely high communication effort to agree on each schedule decision or in an overly restrictive execution model where on-line scheduling, arbitrary preemptions, and nonidentically replicated task sets are not allowed. To overcome these restrictions, a new method, called timed messages, is introduced. Timed messages guarantee deterministic operation by presenting consistent message versions to the replicated tasks. This approach is based on simulated common knowledge and a sparse time base. Timed messages are very effective since they neither require communication between the local scheduler nor do they restrict usage of on-line flexible scheduling, preemptions and nonidentically replicated task sets.