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Biometrics on mobile devices has attracted a lot of attention in recent years as it is considered a user-friendly authentication method. This interest has also been motivated by the success of Deep Learning (DL). Architectures based on Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have been established to be convenient for the task, improving the performance and robustness in comparison to traditional machine learning techniques. However, some aspects must still be revisited and improved. To the best of our knowledge, this is the first article that intends to explore and propose novel gait biometric recognition systems based on Transformers, which currently obtain state-of-the-art performance in many applications. Several state-of-the-art architectures (Vanilla, Informer, Autoformer, Block-Recurrent Transformer, and THAT) are considered in the experimental framework. In addition, new configurations of the Transformers are proposed to further increase the performance. Experiments are carried out using the two popular public databases whuGAIT and OU-ISIR. The results achieved prove the high ability of the proposed Transformer, outperforming state-of-the-art CNN and RNN architectures.