Y Event log anomaly detection aims at identifying anomalous information in the logs generated by the execution of business processes. While several techniques for detecting trace-level anomalies in event logs in offline settings, i.e., when event logs are processed as a batch, have appeared recently in the literature, such techniques are currently lacking for online settings, i.e., when events are processed as a stream. Event log anomaly detection in online settings can be crucial for discovering anomalies in process execution as soon as they occur and, consequently, allowing to take early corrective actions. Moreover, it is also crucial for creating models that can adapt to concept drift in the process generating the events. This paper describes a novel approach to event log anomaly detection in process event streams: we define a general framework in which different anomaly detection methods can be plugged in and we propose and evaluate our own method based on statistical leverage. The leverage is an information-theoretic measure that has been used extensively in statistics to identify outliers and it has been adapted in this paper to the specific scenario of event streams. The proposed approach has been evaluated on artificial and real event streams and also on artificial event streams characterised by concept drift. (C) 2021 Elsevier Ltd. All rights reserved.