Epilepsy is a chronic brain disorder which manifests as recurrent seizures. Electroencephalogram (EEG) signals are generally analyzed to study the characteristics of epileptic seizures. In this work, we propose a method for the automated classification of EEG signals into normal, interictal and ictal classes using Continuous Wavelet Transform (CWT), Higher Order Spectra (HOS) and textures. First the CWT plot was obtained for the EEG signals and then the HOS and texture features were extracted from these plots. Then the statistically significant features were fed to four classifiers namely Decision Tree (DT), K-Nearest Neighbor (KNN), Probabilistic Neural Network (PNN) and Support Vector Machine (SVM) to select the best classifier. We observed that the SVM classifier with Radial Basis Function (RBF) kernel function yielded the best results with an average accuracy of 96%, average sensitivity of 96.9% and average specificity of 97% for 23.6 s duration of EEG data. Our proposed technique can be used as an automatic seizure monitoring software. It can also assist the doctors to cross check the efficacy of their prescribed drugs.