The electroencephalogram (EEG) signal plays an important role in the diagnosis of epilepsy. The EEG recordings of the ambulatory recording systems generate very lengthy data and the 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 proposes a neural-network-based automated epileptic EEG detection system that uses approximate entropy (ApEn) as the input feature. ApEn is a statistical parameter that measures the predictability of the current amplitude values of a physiological signal based on its previous amplitude values. It is known that the value of the ApEn drops sharply during an epileptic seizure and this fact is used in the proposed system. Two different types of Neural Networks, namely, Elman and probabilistic neural networks, are considered in this paper. ApEn is used for the first time in the proposed system for the detection of epilepsy using neural networks. It is shown that the overall accuracy values as high as 100% can be achieved by using the proposed system