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We discuss the problem of soft errors in asynchronous burst mode machines (ABMMs) and we propose two solutions. The first solution is an error tolerance approach, which leverages the inherent functionality of Muller C-elements, along with a variant of duplication, to suppress all transient errors. The proposed method is more robust and less expensive than the typical Triple Modular Redundancy (TMR) error tolerance method and often even less expensive than previously proposed concurrent error detection (CED) methods, which only provide detection but no correction. The second solution is an error mitigation approach, which leverages a newly devised soft error susceptibility assessment method for ABMMs, along with partial duplication, to suppress a carefully chosen subset of transient errors. Three progressively more powerful options for partial duplication select among individual gates, complete state/output logic cones, or partial state/output logic cones, and enable exploration of the trade-off between the achieved soft error susceptibility reduction and the incurred area overhead.