High-resolution modelling, for the first time, is used to study the basic hydrodynamics of the Turkish Straits System (TSS). Hydraulic controls in the Bosphorus and Dardanelles Straits are found to be essential in determining the coupled response of the TSS, which directly influences the interaction between the Mediterranean and Black Seas. The mixed baroclinic-barotropic response of the system is investigated as a function of the net barotropic flux and density stratification imposed at external boundaries, in the absence of atmospheric and tidal effects. The intense surface jet issuing from the Bosphorus is found to drive the basin-wide circulation of the Marmara Sea, varying with the net flux. The temporal response of the Bosphorus and Dardanelles Straits picks up rather fast, within a day or two, thanks to hydraulic controls within straits, while the surface currents in the Marmara Sea only approach steady state after a few months. Model stratification and circulation features are validated against independent measurements and a stand-alone model of the Bosphorus.