Cores acquired by the ANDRILL McMurdo Ice Shelf Project (AND-1B) provide the basis for a new sedimentation model for glacimarine depositional sequences that reflect cyclic glacial–interglacial fluctuations of a marine-based ice sheet in the western Ross Embayment over the past 2.0 Ma. Notwithstanding periodic erosion during advances of the ice sheet, uncertainties inherent to the sedimentological interpretation, and a limited number of chronological datums, it is clear that subglacial to grounding-zone sedimentation was dominant at the AND-1B site during the Late Pleistocene with interglacials being represented only by thin intervals of ice-shelf sediment. Each sequence is characterised by subglacial, massive diamictite that pass upwards into glacimarine diamictites and mudstones. This provides the first direct evidence that the marine-based Antarctic Ice Sheet has oscillated between a grounded and floating state at least 7 times in the Ross Embayment over the last 780ka, implying a Milankovitch orbital influence. An unconformity in AND-1B, that spans most (∼200 kyr) of the Mid-Pleistocene Transition is inferred to represent widespread expansion of a marine-based ice sheet in the Ross Embayment at 0.8 Ma. Prior to 1.0 Ma, interglacial periods are characterised by open-water conditions at the drill site with high abundances of volcanoclastic deposits and occasional diatomaceous sediments. These may have responded to precession (∼20-kyr) or obliquity (∼40-kyr) orbital control. The occurrence of 6.7 m of phonolitic glass reworked from Mt Erebus in interglacial deposits beneath Last Glacial Maximum till requires open ocean or ice shelf conditions in the western Ross Sea around the drill site within the past 250 ka and implies a Ross Ice Shelf similar to or less extensive than today during Marine Isotope Stage 7 or 5.