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Today, epilepsy keeps its importance as a major brain disorder. However, although some devices such as magnetic resonance (MR), brain tomography (BT) are used to diagnose the structural disorders of brain, for observing some special illnesses especially such as epilepsy, EEG is routinely used for observing the epileptic seizures, in neurology clinics. In our study, we aimed to classify the EEG signals and diagnose the epileptic seizures directly by using wavelet transform and an artificial neural network model. EEG signals are separated into δ, θ, α, and β spectral components by using wavelet transform. These spectral components are applied to the inputs of the neural network. Then, neural network is trained to give three outputs to signify the health situation of the patients.