The aim of this work is to develop a computer model capable of simulating the water mass circulation in the Aegean Sea. There is historical, phenomenological and recent experimental evidence of important hydrographical features whose causes have been variably identified as the highly complex bathymetry, the extreme seasonal variations in temperature, the considerable fresh water fluxes, and the large gradients in salinity or temperature across neighbouring water masses (Black Sea and Eastern Mediterranean). In the approach taken here, physical processes are introduced into the model one by one. This method reveals the parameters responsible for permanent and seasonal features of the Aegean Sea circulation. In the first part of the work reported herein, wind-induced circulation appears to be seasonally invariant. This yearly pattern is overcome by the inclusion of baroclinicity in the model in the form of surface thermohaline fluxes. The model shows an intricate pattern of sub-basin gyres and locally strong currents, permanent or seasonal, in accord with the experimental evidence.