A novel wavelet-chaos-neural network methodology is presented for classification of electroencephalograms (EEGs) into healthy, ictal, and interictal EEGs. Wavelet analysis is used to decompose the EEG into delta, theta, alpha, beta, and gamma sub-bands. Three parameters are employed for EEG representation: standard deviation (quantifying the signal variance), correlation dimension, and largest Lyapunov exponent (quantifying the non-linear chaotic dynamics of the signal). The classification accuracies of the following techniques are compared: (1) unsupervised k-means clustering; (2) linear and quadratic discriminant analysis; (3) radial basis function neural network; (4) Levenberg-Marquardt backpropagation neural network (LMBPNN). To reduce the computing time and output analysis, the research was performed in two phases: band-specific analysis and mixed-band analysis. In phase two, over 500 different combinations of mixed-band feature spaces consisting of promising parameters from phase one of the research were investigated. It is concluded that all three key components of the wavelet-chaos-neural network methodology are important for improving the EEG classification accuracy. Judicious combinations of parameters and classifiers are needed to accurately discriminate between the three types of EEGs. It was discovered that a particular mixed-band feature space consisting of nine parameters and LMBPNN result in the highest classification accuracy, a high value of 96.7%.