Title: Compensation-Aware Runtime Monitoring Abstract: To avoid large overheads induced by runtime monitoring, the use of asynchronous log-based monitoring is sometimes adopted --- even though this implies that the system may proceed further despite having reached an anomalous state. Any actions performed by the system after the error occurring are undesirable, since for instance, an unchecked malicious user may perform unauthorized actions. Since stopping such actions is not feasible, in this paper we investigate the use of compensations to enable the undoing of actions, thus enriching asynchronous monitoring with the ability to restore the system to the original state in which the anomaly occurred. Furthermore, we show how allowing the monitor to adaptively synchronise and desynchronise with the system is also possible and report on the use of the approach on an industrial case study of a financial transaction system.