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The effects of transient failures in sequential modules in systems using triple modular redundancy (TMR) cannot be neglected. A transient may place a sequential machine in an erroneous state, and the state may remain erroneous long after the transient has disappeared. We show that the state of a sequential machine can be restored after a transient if and only if the machine has a synchronizing sequence. If synchronizing sequences occur periodically during normal operation of the system, then multiple transients spaced out in time can be tolerated. System structures that have synchronizing sequences are discussed.