In order to enhance the reliability of power systems, a continuous monitoring of the network to detect and clear disturbances is crucial. Fast detection and isolation of disturbances can prevent equipment damage, downtime and other adverse effects associated with their occurrence. The focus of this project is on the detection and classification of two non-linear, complex and severe disturbances: ferroresonance and arcing faults. These disturbances are detected and classified by continuous signal processing of the three-phase voltage and current signals. The models of these disturbances are simulated in EMTP and the three-phase voltage and current are extracted. The extracted data are pre-processed using the discrete wavelet transform (DWT) to extract fault signatures and features used in classifying the disturbances. A decision tree classifier is trained with the extracted features and it is able to detect and classify a disturbance as either ferroresonance or arcing faults using an adaptive time based on the disturbance class. The computational burden in the detection and classification process is reduced by using the superimposed component of the voltage and current to detect transient inceptions prior to classification. Adaptive dead time is adopted to classify the sustained period of the ferroresonance signals and to detect the extinction time of the secondary arc. The results show that the proposed methodology can detect the different ferroresonance modes and arcing faults with 99.8 % accuracy within 100 ms and classify the sustained modes afterwards.