The Strait of Gibraltar limits the exchange between the Atlantic and the Mediterranean Sea and therefore plays an important role in determining the water properties of the evaporation-dominated Mediterranean Sea. On the other hand, the strait dynamics depends on the boundary conditions set by the basin. To investigate this fundamental feedback between strait and basin processes, a 3-box model of the Mediterranean with a hydraulically controlled strait was programmed. It accommodates both maximal and submaximal strait exchange and does not impose steady state budget constraints, making it particularly useful for investigating transitional and non-equilibrium situations. The model is used in an explorative study to find new dynamical aspects of the system. First, the response of the system to changing air-sea-fluxes is modelled. Increasing evaporation shifts the steady state of the system to a more saline and - as a secondary effect - slightly warmer state. Increased heat loss leads to a colder and slightly less saline basin. Besides shifting the steady state, changes in heat flux and net evaporation can also lead to a nonlinear response in which the pycnocline deepens considerably for a transitional period of decades or centuries before returning to its steady state depth. Second, the effect of rising sea levels since the Last Glacial Maximum (18kyr BP) was modelled. At times of rapid sea level rise, the long residence time leads to stronger stratification and reduced circulation in the basin, providing a possible mechanism for the formation of sapropel S1. Finally the effect of mixing in the hydraulic jump between the Mediterranean and the Strait of Gibraltar is included in the model. The entrainment of inflowing water into the outflow reduces the effective exchange between Atlantic and Mediterranean, and the system develops multiple equilibria. After a comparatively short perturbation (e.g. a 20% larger evaporation for 10 years), the system can move from the stable, well-ventilated state to an almost stagnant meta-stable state which persists for centuries before the well-ventilated state is reestablished.