The unpredictability of the occurrence of epileptic seizures makes it difficult to detect and treat this condition effectively. An automatic system that characterizes epileptic activities in EEG signals would allow patients or the people near them to take appropriate precautions, would allow clinicians to better manage the condition, and could provide more insight into these phenomena thereby revealing important clinical information. Various methods have been proposed to detect epileptic activity in EEG recordings. Because of the nonlinear and dynamic nature of EEG signals, the use of nonlinear Higher Order Spectra (HOS) features is a seemingly promising approach. This paper presents the methodology employed to extract HOS features (specifically, cumulants) from normal, interictal, and epileptic EEG segments and to use significant features in classifiers for the detection of these three classes. In this work, 300 sets of EEG data belonging to the three classes were used for feature extraction and classifier development and evaluation. The results show that the HOS based measures have unique ranges for the different classes with high confidence level (p-value < 0.0001). On evaluating several classifiers with the significant features, it was observed that the Support Vector Machine (SVM) presented a high detection accuracy of 98.5% thereby establishing the possibility of effective EEG segment classification using the proposed technique.