This paper overviews various approaches to the problem of detecting anomalous behavior within the framework of intrusion detection systems using non-signature-based methods. Each described algorithm has different underlying approach but they all show effective results in the problems of assessing the availability of the wrongfulness of the actions of an authorized user inside an information system. The techniques discussed in the paper use Markov Chains, Hierarchical Hidden Markov Models, algorithms for filtering noise in the signal in the intrusion detection problem, as well as methods based on ontology and agents. Finally, the experimental system developed at Caldas University, Colombia is considered that uses a lot of different approaches aimed to increase anomaly detection efficiency.