The stability of the glacial thermohaline circulation (THC) with respect to North Atlantic freshwater input is examined using a global ocean general circulation model. It is found that the quasi-equilibrium hysteresis behaviour is much less pronounced under glacial conditions than under present-day conditions, and the existence of multiple equilibria requires an anomalous freshwater inflow. The results may help to assess the effect of iceberg invasions and meltwater events, suggesting that the THC is prone to instability during a deglaciation phase when the Atlantic meridional overturning is weakened. Under full glacial conditions, however, the THC is mono-stable and even extreme freshwater pulses are unable to exert a persistent effect on the conveyor.