105 synthetic time series replicating GNSS 3D position series are analyzed independently by nine different groups within the RENAG consortium in order to characterize the variability in estimations of long-term velocities. The main objective is not a detailed study of the parameters and sources controlling velocity variations, but simply to establish first-order conclusions regarding the uncertainties on GNSS velocity estimations as a function of the different analysis methods and software. Because the true velocities are known, our results are presented in terms of velocity biases (i.e. deviations of the estimated velocities relative to the expected values). Statistics on these biases can then be used as indicators of the potential precision of actual GNSS velocities. To first order, the nine methods and software of time series analysis provide horizontal (resp. vertical) velocity estimations at precisions better than 1.0 mm/a (resp. 2.0 mm/a). None of the tested methods or software clearly stands out as significantly better or worse than the others. However, a group of four solutions (including the unweighted average of all nine solutions) provides systematically better results than the others. They are based on a standard time series analysis using a least-square inversion of a parametric model (velocity, seasonal terms, offsets) with either automatic and manual offset detection methods. For time series with noise and duration characteristics corresponding to classical GNSS data (e.g., RENAG-RESIF stations), the velocity biases (and thus potential GNSS velocity precision) are characterized by the following statistics: • Medians ca. 0.1 mm/a (horizontal components) and 0.1–0.3 mm/a (vertical component). • 95th percentiles ca. 0.2–0.7 mm/a (horizontal components) and 0.5–2.0 mm/a (vertical component). • RMS (root-mean-square) ca. 0.1–0.3 mm/a (horizontal components) and 0.3–0.9 mm/a (vertical component). In addition to the variability of velocity estimations as a function of the analysis methods, first order information can be derived regarding the solution combination and velocity uncertainties: • The unweighted average of all nine analyses yields results systematically in the upper tier of all individual solutions. • Formal velocity uncertainties (standard errors) calculated on the basis of colored- noise models are statically representative of the velocity biases. • In contrast, formal velocity uncertainties (standard errors) calculated using other methods (white noise or statistical variance) are not representative of the velocity biases (resp. significantly too low or too high).