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Seasonal signals in geodetic time-series have long been recognized to be associated with environmental phenomena such as polar motion, atmospheric loading, groundwater loading and other hydrological processes. Modelling these periodic signals is crucial for the geophysical interpretation of these time-series. The most common approach used for resolving seasonal (annual and semi-annual) signals is their approximation by sinusoidal functions with constant amplitudes. However, because of their environmental source, seasonal signals are likely to be quasi-periodic. In this study, we investigate a Gaussian process (GP) to model quasi-periodic signals in geodetic time-series, a flexible method that allows capturing the variability structure in the data using covariance functions. We use the Markov Chain Monte Carlo method to evaluate the posterior probability density function. To test its effectiveness, we apply this method to a synthetic time-series in the presence of time-correlated noise. We find that the GP model provides a better fit to the time-series, resulting in time-series residuals with fewer systematic effects. We use the GP model to estimate the secular velocity of selected GPS sites from Antarctica and Alaska, as well as an example of Gravity Recovery and Climate Experiment time-series. The Bayesian aspect of the GP model allows inferring the linear velocity ensemble in the vicinity of the true solution while taking into account the quasi-periodic systematics in the time-series. [ABSTRACT FROM AUTHOR]