Stable isotope records of benthic foraminifera from ODP Site 1264 in the southeastern Atlantic Ocean are presented which resolve the latest Oligocene to early Miocene (∼24-19 Ma) climate changes at high temporal resolution (<3 kyr). Using an inverse modelling technique, we decomposed the oxygen isotope record into temperature and ice volume and found that the Antarctic ice sheet expanded episodically during the declining phase of the long-term (∼400 kyr) eccentricity cycle and subsequent low short-term (∼100 kyr) eccentricity cycle. The largest glaciations are separated by multiple long-term eccentricity cycles, indicating the involvement of a non-linear response mechanism. Our modelling results suggest that during the largest (Mi-1) event, Antarctic ice sheet volume expanded up to its present-day configuration. In addition, we found that distinct ∼100 kyr variability occurs during the termination phases of the major Antarctic glaciations, suggesting that climate and ice-sheet response was more susceptible to short-term eccentricity forcing at these times. During two of these termination-phases, δ 18O bottom water gradients in the Atlantic ceased to exist, indicating a direct link between global climate, enhanced ice-sheet instability and major oceanographic reorganisations.