For classification of action potential shapes in multineuron recordings, we present a spike sorting system employing independent component analysis (ICA) and an unsupervised artificial neural network (Kohonen's self-organizing map, SOM). We focus on how ICA in the first stage of the spike sorting system can be used to address specific problems arising in recordings using multielectrode arrays in the CNS. Using real data recorded from the pontine nuclei in rats and simulated data, we evaluate the performance of several ICA algorithms to remove cross-talk between electrodes using data from continuous recording (or simulation). When using cut-out data, the standard format of extracellular spike recordings, new problems emerge and robust algorithms are needed. We demonstrate that several ICA algorithms show a good performance on cut-out data from multielectrode array recordings (simulated and real data). In tetrode recordings the same neuron is purposely recorded by several electrodes simultaneously and we show, how independent component analysis can be used in this case to identify redundant information and hence to compress relevant information, improving subsequent clustering of a SOM.