The recording of seizures is of primary interest in the evaluation of epileptic patients. Seizure is the phenomenon of rhythmicity discharge from either a local area or the whole brain and the individual behavior usually lasts from seconds to minutes. Since seizures, in general, occur infrequently and unpredictably, automatic detection of seizures during long-term electroencephalograph (EEG) recordings is highly recommended. As EEG signals are nonstationary, the conventional methods of frequency analysis are not successful for diagnostic purposes. This paper presents a method of analysis of EEG signals, which is based on time-frequency analysis. Initially, selected segments of the EEG signals are analyzed using time-frequency methods and several features are extracted for each segment, representing the energy distribution in the time-frequency plane. Then, those features are used as an input in an artificial neural network (ANN), which provides the final classification of the EEG segments concerning the existence of seizures or not. We used a publicly available dataset in order to evaluate our method and the evaluation results are very promising indicating overall accuracy from 97.72% to 100%.