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In recent years, automatic sleep staging methods have achieved competitive performance using electroencephalography (EEG) signals. However, the acquisition of EEG signals is cumbersome and inconvenient. Therefore, we propose a novel sleep staging approach using electrooculogram (EOG) signals, which are more convenient to acquire than the EEG. A two-scale convolutional neural network first extracts epoch-wise temporary-equivalent features from raw EOG signals. A recurrent neural network then captures the long-term sequential information. The proposed method was validated on 101 full-night sleep data from two open-access databases, the montreal archive of sleep studies and Sleep-EDF, achieving an overall accuracy of 81.2 and 76.3%, respectively. The results are comparable to those models trained with EEG signals. In addition, comparisons with six state-of-the-art methods further demonstrate the effectiveness of the proposed approach. Overall, this study provides a new avenue for sleep monitoring.