A coupled climate-ice-sheet model is used to investigate the response of climate at the millennial time scale under several global warming long-term scenarios, stabilized at different levels ranging from 2 to 7 times the pre-industrial CO2 level. The climate response is mainly analyzed in terms of changes in temperature, oceanic circulation, and ice-sheet behaviour. For the 4 x CO2 scenario, the climate response appears to be highly non-linear: abrupt transitions occur in the Southern Ocean deep water formation strength with a period of about 1200 yr. These millennial oscillations do not occur for both lower and larger CO2 levels. We show that these transitions are associated with internal oscillations of the Southern Ocean, triggered by the Antarctic freshwater budget. We first analyse the oscillatory mechanism. Secondly, through a series of 420 sensitivity experiments we also explore the range of temperature and freshwater flux for which such oscillations can be triggered.