Accurate automatic spike detection is highly beneficial to clinical assessment of epileptic electroencephalogram (EEG) data. In this paper, a new two-stage approach is proposed for epileptic spike detection. First, the k-point nonlinear energy operator (k-NEO) is adopted to detect all possible spike candidates, then a newly proposed spike model with slow wave features is applied to these candidates for spike classification. Experimental results show that the proposed system, using the AdaBoost classifier, outperforms the conventional method in both two- and three-class EEG pattern classification problems. The proposed system not only achieves better accuracy for spike detection, but also provides new ability to differentiate between spikes and spikes with slow waves. Though spikes with slow waves occur frequently in epileptic EEGs, they are not used in conventional spike detection. Identifying spikes with slow waves allows the proposed system to have better capability for assisting clinical neurologists in routine EEG examinations and epileptic diagnosis.