We examine the source mechanisms and depths of the largest earthquake that has occurred in the vicinity of Cyprus in the last 50 years, the 1996 October 9 earthquake (Mw= 6.8) and its principal aftershock on October 10 (Mw= 5.8). Being the first large event in the area for which seismic data from the global digital network are available, it provides an excellent opportunity to study the complex tectonic processes of the eastern Mediterranean. We modelled the source mechanisms and depths of the earthquakes by a least‐squares body waveform fitting procedure. The waveform fits resulting from our minimum‐misfit solutions are considerably better than those predicted by previous studies. We show strong evidence that both events were at depths of 76–85 km rather than 20–30 km, as has been suggested by other studies. These earthquakes form a group indicating that the Mediterranean lithosphere south of the Hellenic and Cyprean arcs is in east–west compression as it is subducted to the north and northeast. We additionally examine the source mechanism and depth of the 1999 August 11 earthquake (Mw= 5.6), which occurred at about 11 km with a reverse dip‐slip mechanism. It probably reflects crustal shortening between the African and Turkish plates.