Multiple equilibria of the climate system, inferred from paleo reconstructions, have also been observed in both ocean-only and coupled ocean-atmosphere general circulation models. These multiple states are thought to be associated with different modes of operation of the meridional overturning circulation in the North Atlantic. It has recently been suggested that the stability of these states depends on the amount of vertical mixing in ocean models. Here we investigate the dependence of the hysteresis behavior of the thermohaline circulation to sub-gridscale mixing processes in the ocean. Using a simplified coupled ocean-atmosphere model we find that both vertical and horizontal diffusivities have considerable influence on the stability of the different circulation modes. They also change the transition points from one circulation pattern to another. Larger vertical diffusivities lead to higher values of additional precipitation into the North Atlantic being necessary to stop the formation of deep water. However, for slightly increased evaporation, the state without deep water formation becomes increasingly unstable for stronger vertical diffusion. Larger values of horizontal mixing lead to a narrowing of the phase space for which two equilibria are stable. These results suggest that it is currently not possible, given the large uncertainty in ocean mixing, to quantitatively determine possible thresholds for the transition of the North Atlantic thermohaline circulation between on and off modes. This presents a policy predicament as it makes it extremely difficult to assign a probability for the future occurrence of such nonlinear climate transition. ¿ 2001 American Geophysical Union