In this work, we explore approaches for detecting anomalies in system event logs. We define the system log anomaly detection problem and research existing methods. We apply the methods to a practical task of detecting anomalous events in logs of file behavior analysis sandbox. To validate results and compare methods we calculate quality metrics on a manually labeled dataset. First, we try an approach based on calculating event document frequency and use it as a baseline. We improve it by creating an event normalization algorithm and significantly reducing the number of false positives. After that, we implement a different approach that involves extracting event features and training random forest and logistic regression models to model a probability of an event belonging to a clean or anomalous log. Finally, we create a sequence model based on a recurrent neural network and use it to detect anomalies in event sequences.