The back-projected independent components (BICs) of single-trial, auditory P300 and contingent negative variation (CNV) evoked potentials (EPs) were derived using independent component analysis (ICA) and cluster analysis. The method was tested in simulation including a study of the electric dipole equivalents of the signal sources. P300 data were obtained from healthy and Alzheimer's disease (AD) subjects. The BICs were of approximately 100 ms duration and approximated positive- and negative-going half-sinusoids. Some positively and negatively peaking BICs constituting the P300 coincided with known peaks in the averaged P300. However, there were trial-to-trial differences in their occurrences, particularly where a positive or a negative BIC could occur with the same latency in different trials, a fact which would be obscured by averaging them. These variations resulted in marked differences in the shapes of the reconstructed, artefact-free, single-trial P300s. The latencies of the BIC associated with the P3b peak differed between healthy and AD subjects (p < 0.01). More reliable evidence than that obtainable from single-trial or averaged P300s is likely to be found by studying the properties of the BICs over a number of trials. For the CNV, BICs corresponding to both the orienting and the expectancy components were found.