An　automatic　detection　system　for　distinguishing　normal,　ictal,　and　interictal　electroencephalogram　(EEG)　signals　is　of　great　help　in　clinical　practice.　This　paper　presents　a　three-class　classification　system　based　on　discrete　wavelet　transform　(DWT)　and　the　nonlinear　sparse　extreme　learning　machine　(SELM)　for　epilepsy　and　epileptic　seizure　detection.　Three-level　lifting　DWT　using　Daubechies　order　4　wavelet　is　introduced　to　decompose　EEG　signals　into　delta,　theta,　alpha,　and　beta　subbands.　Considering　classification　accuracy　and　computational　complexity,　the　maximum　and　standard　deviation　values　of　each　subband　are　computed　to　create　an　eight-dimensional　feature　vector.　After　comparing　five　multiclass　SELM　strategies,　the　one-against-one　strategy　with　the　highest　accuracy　is　chosen　for　the　three-class　classification　system.　The　performance　of　the　designed　three-class　classification　system　is　tested　with　publicly　available　epilepsy　dataset.　The　results　show　that　the　system　achieves　high　enough　classification　accuracy　by　combining　the　SELM　and　DWT　and　reduces　training　and　testing　time　by　decreasing　computational　complexity　and　feature　dimension.　With　excellent　classification　performance　and　low　computation　complexity,　this　three-class　classification　system　can　be　utilized　for　practical　epileptic　EEG　detection,　and　it　offers　great　potentials　for　portable　automatic　epilepsy　and　seizure　detection　system　in　the　future　hardware　implementation.