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The growing application of deep neural networks in safety-critical domains makes the analysis of faults that occur in such systems of enormous importance. In this paper we introduce a large taxonomy of faults in deep learning (DL) systems. We have manually analysed 1059 artefacts gathered from GitHub commits and issues of projects that use the most popular DL frameworks (TensorFlow, Keras and PyTorch) and from related Stack Overflow posts. Structured interviews with 20 researchers and practitioners describing the problems they have encountered in their experience have enriched our taxonomy with a variety of additional faults that did not emerge from the other two sources. Our final taxonomy was validated with a survey involving an additional set of 21 developers, confirming that almost all fault categories (13/15) were experienced by at least 50% of the survey participants.