Transformers are used in time series applications for forecasting qualitative variables and, in minor proportion, for quantitative variables. The cryptocurrency market data is highly noisy and nonlinear, and it conditions the effectiveness and efficiency of the models that can be used to forecast their price, making this task a challenge, as shown in the technical literature. Therefore, the present study proposes the following alternative: thoroughly training, testing, and validating models based on Transformer architecture combined with LSTM and GRU neural networks. According to the results, forecasting BTC Bitcoin (BTC) and Ethereum (ETH) prices are promising using data from 2017–2024, a period of high price variation, and compared with equivalent studies. The subjacent idea in this study is that if appropriately modeled, cryptocurrency prices can be predicted reasonably accurately, although the cryptocurrency market is complex to model.