Epileptic seizures are manifestations of epilepsy. Careful analyses of the electroencephalograph (EEG) records can provide valuable insight and improved understanding of the mechanisms causing epileptic disorders. The detection of epileptiform discharges in the EEG is an important component in the diagnosis of epilepsy. As EEG signals are non-stationary, the conventional method of frequency analysis is not highly successful in diagnostic classification. This paper deals with a novel method of analysis of EEG signals using wavelet transform and classification using artificial neural network (ANN) and logistic regression (LR). Wavelet transform is particularly effective for representing various aspects of non-stationary signals such as trends, discontinuities and repeated patterns where other signal processing approaches fail or are not as effective. Through wavelet decomposition of the EEG records, transient features are accurately captured and localized in both time and frequency context. In epileptic seizure classification we used lifting-based discrete wavelet transform (LBDWT) as a preprocessing method to increase the computational speed. The proposed algorithm reduces the computational load of those algorithms that were based on classical wavelet transform (CWT). In this study, we introduce two fundamentally different approaches for designing classification models (classifiers) the traditional statistical method based on logistic regression and the emerging computationally powerful techniques based on ANN. Logistic regression as well as multilayer perceptron neural network (MLPNN) based classifiers were developed and compared in relation to their accuracy in classification of EEG signals. In these methods we used LBDWT coefficients of EEG signals as an input to classification system with two discrete outputs: epileptic seizure or non-epileptic seizure. By identifying features in the signal we want to provide an automatic system that will support a physician in the diagnosing process. By applying LBDWT in connection with MLPNN, we obtained novel and reliable classifier architecture. The comparisons between the developed classifiers were primarily based on analysis of the receiver operating characteristic (ROC) curves as well as a number of scalar performance measures pertaining to the classification. The MLPNN based classifier outperformed the LR based counterpart. Within the same group, the MLPNN based classifier was more accurate than the LR based classifier.