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Automatic detection and classification of dynamic hand gestures in real-world systems intended for human computer interaction is challenging as: 1) there is a large diversity in how people perform gestures, making detection and classification difficult; 2) the system must work online in order to avoid noticeable lag between performing a gesture and its classification; in fact, a negative lag (classification before the gesture is finished) is desirable, as feedback to the user can then be truly instantaneous. In this paper, we address these challenges with a recurrent three-dimensional convolutional neural network that performs simultaneous detection and classification of dynamic hand gestures from multi-modal data. We employ connectionist temporal classification to train the network to predict class labels from in-progress gestures in unsegmented input streams. In order to validate our method, we introduce a new challenging multi-modal dynamic hand gesture dataset captured with depth, color and stereo-IR sensors. On this challenging dataset, our gesture recognition system achieves an accuracy of 83.8%, outperforms competing state-of-the-art algorithms, and approaches human accuracy of 88.4%. Moreover, our method achieves state-of-the-art performance on SKIG and ChaLearn2014 benchmarks.