In the last couple of decades, tremendous progress has been achieved in developing robotic telescopes and, as a result, sky surveys (both terrestrial and space) have become the source of a substantial amount of new observational data. These data contain a lot of information about binary stars, hidden in their light curves. With the huge amount of astronomical data gathered, it is not reasonable to expect all the data to be manually processed and analyzed. Therefore, in this paper, we focus on the automatic classification of eclipsing binary stars using deep learning methods. Our classifier provides a tool for the categorization of light curves of binary stars into two classes: detached and over-contact. We used the ELISa software to obtain synthetic data, which we then used for the training of the classifier. For evaluation purposes, we collected 100 light curves of observed binary stars, in order to evaluate a number of classifiers. We evaluated semi-detached eclipsing binary stars as detached.The best-performing classifier combines bidirectional Long Short-Term Memory (LSTM) and a one-dimensional convolutional neural network, which achieved 98% accuracy on the evaluation set. Omitting semi-detached eclipsing binary stars, we could obtain 100% accuracy in classification.