Statistically optimal methods for identifying single unit activity in multiple unit recordings are discussed. These methods take into account both the nerve impulse waveforms and the firing patterns of the units. A generalized least-squares fit procedure is shown to be the optimal recognition scheme under some reasonable statistical assumptions, but the amount of computation becomes prohibitively large when the method is applied to the problem of sorting superimposed waveforms. A linear filter technique which relies on simultaneous recording from several electrodes is shown to give good separation of superimposed waveforms. An iterative recognition procedure can be applied to improve the results and reduce the number of recording electrodes required.