Brief fragments of sleep shorter than 15 s are defined as microsleep episodes (MSEs), often subjectively perceived as sleepiness. Their main characteristic is a slowing in frequency in the electroencephalogram (EEG), similar to stage N1 sleep according to standard criteria. The maintenance of wakefulness test (MWT) is often used in a clinical setting to assess vigilance. Scoring of the MWT in most sleep-wake centers is limited to classical definition of sleep (30 s epochs), and MSEs are mostly not considered in the absence of established scoring criteria defining MSEs but also because of the laborious work. We aimed for automatic detection of MSEs with machine learning, i.e., with deep learning based on raw EEG and EOG data as input. We analyzed MWT data of 76 patients. Experts visually scored wakefulness, and according to recently developed scoring criteria MSEs, microsleep episode candidates (MSEc), and episodes of drowsiness (ED). We implemented segmentation algorithms based on convolutional neural networks (CNNs) and a combination of a CNN with a long-short term memory (LSTM) network. A LSTM network is a type of a recurrent neural network which has a memory for past events and takes them into account. Data of 53 patients were used for training of the classifiers, 12 for validation and 11 for testing. Our algorithms showed a good performance close to human experts. The detection was very good for wakefulness and MSEs and poor for MSEc and ED, similar to the low inter-expert reliability for these borderline segments. We performed a visualization of the internal representation of the data by the artificial neuronal network performing best using t-distributed stochastic neighbor embedding (t-SNE). Visualization revealed that MSEs and wakefulness were mostly separable, though not entirely, and MSEc and ED largely intersected with the two main classes. We provide a proof of principle that it is feasible to reliably detect MSEs with deep neuronal networks based on raw EEG and EOG data with a performance close to that of human experts. The code of the algorithms (https://github.com/alexander-malafeev/microsleep-detection) and data (https://zenodo.org/record/3251716) are available.