Abstract: We point out that if independent component analysis or blind source separation is performed in high dimensions with an insufficient sample size, this may lead to generation of artefactual source signals due to overlearning (or overfitting). Such artefactual source signals are practically zero almost everywhere, expect at the point of a single spike or bump. The existence of strong time-correlations in the data increases the probability of the occurence of the artefacts. These results are essentially independent of the particular algorithm used for ICA.