A primary-backup replication capability is disclosed. A primary process and a backup process participate in a synchronization process configured to synchronize state information of the primary and backup processes. The synchronization process operates in periods of time referred to as epochs. During the current epoch, the primary process computes state update information representing changes to the state information of the primary process since a previous epoch, and also buffers output messages generated during the current epoch in an associated output buffer dedicated for use in the current epoch. The primary process initiates a new epoch independent of receiving, from the backup process, a state update acknowledgement for the previous epoch. The output messages buffered for the current epoch are released from the associated output buffer after the primary process receives a state update acknowledgment for the current epoch and all output buffers of all previous epochs are empty.