We are living in an information age where all our personal data and systems are connected to the Internet and accessible from more or less anywhere in the world. Such systems can be prone to cyber-attacks; therefore the monitoring and identification of cyber-attacks play a significant role in preventing the abuse of our data and systems. The majority of such systems proposed in the literature are based on a model/classifiers built with the help of classical/off-line learning methods on a learning data set. Since cyber-attacks evolve over time such models or classifiers sooner or later become outdated. To keep a proper system functioning the models need to be updated over a period of time. When dealing with models/classifiers learned by classical off-line methods, this is an expensive and time-consuming task. One way to keep the models updated is to use evolving methodologies to learn and adapt the models in an on-line manner. Such methods have been developed, extensively studied and implemented for regression problems. The presented paper introduces a novel evolving possibilistic Cauchy clustering (eCauchy) method for classification problems. The given method is used as a basis for large-scale monitoring of cyber-attacks. By using the presented method a more flexible system for detection of attacks is obtained. The approach was tested on a database from 1999 KDD intrusion detection competition. The obtained results are promising. The presented method gives a comparable degree of accuracy on raw data to other methods found in the literature; however, it has the advantage of being able to adapt the classifier in an on-line manner. The presented method also uses less labeled data to learn the classifier than classical methods presented in the literature decreasing the costs of data labeling. The study is opening a new possible application area for evolving methodologies. In future research, the focus will be on implementing additional data filtering and new algorithms to optimize the classifier for detection of cyber-attacks.