Electroencephalogram (EEG) signal plays an important role in the diagnosis of epilepsy. The long-term EEG recordings of an epileptic patient obtained from the ambulatory recording systems contain a large volume of EEG data. Detection of the epileptic activity requires a time consuming analysis of the entire length of the EEG data by an expert. The traditional methods of analysis being tedious, many automated diagnostic systems for epilepsy have emerged in recent years. This paper discusses an automated diagnostic method for epileptic detection using a special type of recurrent neural network known as Elman network. The experiments are carried out by using time-domain as well as frequency-domain features of the EEG signal. Experimental results show that Elman network yields epileptic detection accuracy rates as high as 99.6% with a single input feature which is better than the results obtained by using other types of neural networks with two and more input features.