This work is dedicated to the study of the climate variability of the Mediterranean Sea, in particular the study of the Eastern Mediterranean Transient (EMT) which occurred in the early 1990s. Simulations of the 1961–2000 period have been carried out with an eddy‐permitting Ocean General Circulation Model of the Mediterranean Sea, driven by realistic interannual high‐resolution air‐sea fluxes. Using different databases for the river runoff, Black Sea inflow, and Atlantic thermohaline characteristics at climatological or interannual scales, we assess the effects of the non‐atmospheric hydrological forcings on the simulation of the interannual variations of the Mediterranean circulation. The evolution of the basin‐scale heat content is in very good agreement with the observations (especially in the surface and intermediate layers), while the agreement is lower for the evolution of the salt content. Convection events in the Aegean Sea are noticed in the simulations between 1972 and 1976, in the late 1980s, and around the EMT period. The formation rates of Cretan Deep Water (CDW) are different during these periods, allowing or preventing the spreading of CDW into the eastern Mediterranean. The sequence of the EMT events is well reproduced: the high winter oceanic surface cooling and net evaporation over the Aegean Sea in the early 1990s, the high amount of dense CDW formed during these winters, and then the overflow and the spreading of this CDW in the eastern Mediterranean. Among the preconditioning processes suggested in the literature, we find that changes in the Levantine surface circulation, possibly induced by the presence in the Cretan Passage of anticyclonic eddies and a lasting period with reduced net precipitation over the eastern Mediterranean, lead to an increase of the salt content of the Aegean Sea. Changes in the Black Sea freshwater inflow or in the characteristic of the Atlantic Water entering at the Gibraltar Strait also modify the thermohaline state of the Aegean Sea before the EMT. But, as none of these preconditioning factors has a lasting impact on lowering the vertical stratification of the Aegean Sea, we conclude that concerning the EMT, the major triggering elements are the atmospheric fluxes and winds occurring in winters 1991–1992 and 1992–1993.