Epileptic seizures are manifestations of epilepsy, which is a serious brain dynamic disorder. The analysis of the electroencephalographic (EEG) recordings provides valuable insight and improved understanding of the mechanisms causing epileptic disorders. An epileptic seizure is usually identified by polyspike activity; rhythmic waves for a wide variety of frequencies and amplitudes as well as spike-and-wave complexes. The detection of all these waveforms in the EEG is a crucial component in the diagnosis of epilepsy. Time-frequency analysis is particularly effective for representing various aspects of nonstationary signals such as trends, discontinuities, and repeated patterns where other signal processing approaches fail or are not as effective. In this paper a novel method of analysis of EEG signals using time-frequency analysis, and classification using artificial neural network, is introduced. EEG segments are analyzed using a time-frequency distribution and then, several features are extracted for each segment representing the energy distribution over the time-frequency plane. The features are used for the training of a neural network. Short-time Fourier transform and several time-frequency distributions are compared. The proposed approach is tested using a publicly available database and satisfactory results are obtained (89-100% accuracy).