In modern communication networks, the integrity of the security is of great importance, since the existence of cyber attacks may lead to disastrous financial and social consequences. The anomaly detection constitutes an essential part of network security. This paper proposes a two-stage procedure to provide a solution regarding the anomaly detection and threat identification. The proposed method is suitable for modern communication networks and upcoming smart networks. The first stage of the method concerns the detection of abnormal incidents and the second stage involves the identification of the type of cyber threats, in case of an attack. The method based on the development of artificial neural network models and the UNSW-NB15 dataset is used to validate the proposed methodology. The experimental results confirm that the proposed method identifies all type of threats in comparison to the already known methods that identify only the threats that appear frequently.