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Modeling station and satellite clocks in the GNSS analysis in order to reduce existing correlations requires a high level of stability for the corresponding clocks. In this contribution, we provide a comprehensive and up-to-date status regarding the stability of on-board clocks of GPS, GLONASS, and Galileo satellites, as well as hydrogen maser stations within the International GNSS Service network. We use exemplary events of irregularities to show which factors need to be taken into account when analyzing a longer period of GNSS clocks. Based on epoch-wise clock biases estimated for different sampling rates (5 min / 30 s) in a daily network solution from May 2023 to April 2024, various stability analyses are carried out. About 60 of the 80 hydrogen maser stations distributed worldwide show a high stability with an average daily standard deviation of less than 75 picoseconds. For the satellite clocks the stability depends mainly on the atomic clock type and the age of the satellite block. In a further stability analysis, the 5-min clock estimates are subjected to a linear regression analysis with different interval lengths. The clock estimates of the younger satellite generations (GPS IIF, GPS IIIA, Galileo FOC) and the highly stable hydrogen maser stations can be well characterized by linear representations; assuming 10 mm as a threshold for the mean regression fit RMS, the maximum interval lengths are two and eight hours, respectively.