We use 576 earthquakes of magnitude, M w, 3.3 to 6.8 that occurred within the region 33° N–42.5° N, 19° E–30° E in the time period 1969 to 2007 to investigate the stability of the relation between moment magnitude, M w, and local magnitude, M L, for earthquakes in Greece and the surrounding regions. We compare M w to M L as reported in the monthly bulletins of the National Observatory of Athens (NOA) and to M L as reported in the bulletins of the Seismological Station of the Aristotle University of Thessaloniki. All earthquakes have been analyzed through regional or teleseismic waveform inversion, to obtain M w, and have measured maximum trace amplitudes on the Wood–Anderson seismograph in Athens, which has been in operation since 1964. We show that the Athens Wood–Anderson seismograph performance has changed through time, affecting the computed by NOA M L by at least 0.1 magnitude units. Specifically, since the beginning of 1996, its east–west component has been recording systematically much larger amplitudes compared to the north–south component. From the comparison between M w and M L reported by Thessaloniki, we also show that the performance of the sensors has changed several times through time, affecting the calculated M L’s. We propose scaling relations to convert the M L values reported from the two centers to M w. The procedures followed here can be applied to other regions as well to examine the stability of magnitude calculations through time.