Today, networks of permanent reference stations are broadly used for the realization of national Geodetic Reference Systems. Furthermore, single-base GNSS positioning is progressively being replaced by network-based techniques like VRS, FKP and MAC. These techniques model the error sources in order to eliminate the distance-dependent errors in relative GNSS geodetic positioning. The effective modelling of the error sources requires highly accurate coordinates of the reference stations. Site displacements can affect the estimation of error models, degrading the performance of the network. Besides monumentation instabilities and other issues, site displacements can also be caused by tectonic activity. Unlike the majority of European countries, Greece is characterized by strong tectonic activity. Moreover, the Greek area extends over different tectonic plates having individual velocities. This results in a complex velocity field. The situation has to be taken into account in the operation of the Hellenic Positioning System (HEPOS), an RTK network consisting of 98 permanent GPS reference stations distributed throughout Greece. HEPOS is operational since the end of 2007. Observations collected at the HEPOS stations for more than two years have been processed in order to estimate the velocity characteristics of each station. This paper describes the processing strategy and presents the results, which reveal an inhomogeneous deformation field. The impact of station displacements on the network operation is discussed.