When recording extracellular neural activity, it is often necessary to distinguish action potentials arising from distinct cells near the electrode tip, a process commonly referred to as spike sorting or action potential sorting. Sorting of neuronal spikes plays a very important role in coding of neural information, which is a prerequisite for studying the brain function. In this paper, five major action potential classification methods including Template Matching, Wavelet Transform, Principal Component Analysis, Back-Propagation (BP) Neural Network, Two-stage Radius Basis Function Network are studied. Under the conditions of different levels of background noise, the performances of these methods are tested. This work may be helpful to choose classification method.