GNSS (Global Navigation Satellite System) time series are indispensable in geodesy, geophysics, and other Earth sciences, and serve as important tools for monitoring crustal deformation, plate tectonics, and other geodynamic phenomena. Analytical methods are used to improve the robustness and data quality of the results obtained from GNSS station position time series. The objective of this paper is to investigate the applicability of deep learning techniques in modeling and prediction studies on GNSS station position time series. The performance of 8 deep learning models, including Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Temporal Convolution Network (TCN), TCN-Leaky ReLU, TCN-Leaky ReLU-LSTM, Bidirectional LSTM, Bidirectional GRU, and Stack-LSTM, are analyzed based on the traditional Least Squares (LS) method and their ability to improve the prediction accuracy on three components of 9 GNSS stations in Western Turkey. The results show that the deep learning methods provide improvements in Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) by 45% and 53% in the East component, 44% and 51% in the North component, and 34% and 41% in the Up component, respectively, compared to the LS model. The study provides a detailed comparative analysis of model performance and demonstrates the performance of the Bi-LSTM and Bi-GRU and GRU models in handling high noise environments and complex transient changes at some stations.