In this study, it has been intended to perform an automatic classification of Electroencephalography (EEG) signals via Artificial Neural Networks (ANN) and to investigate these signals using Wavelet Transform (WT) for diagnosing epilepsy syndrome. EEG signals have been decomposed into frequency sub-bands using WT and a set of feature vectors which were extracted from the sub-bands. Dimensions of these feature vectors have been reduced via Principal Component Analysis (PCA) method and then classified as epileptic or healthy using Multilayer Perceptron (MLP) and ELMAN ANN. Performance evaluation of the used ANN models have been carried out by performing Receiver Operation Characteristic (ROC) analysis.