1. Institute of Geological and Nuclear Sciences, PO Box 30368, Lower Hutt, New Zealand
2. School of Earth Sciences, James Cook University, Townsville, Queensland 4811, Australia
3. Antarctic Research Centre, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
4. Department of Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, UK
5. Department of Geosciences, University of Nebraska, Lincoln, Nebraska 68588-0340, USA
6. Institut für Geowissenschaftliche Gemeinschaftsaufgaben, Stilleweg 2, D-30655 Hannover, Germany
7. Istituto di Scienze del Mare, Universitá degli Studi di Ancona, Via Brecce Bianche, 60131 Ancona, Italy
8. National Institute of Water and Atmospheric Research, PO Box 14901, Wellington, New Zealand
9. Department of Earth Sciences, University of Queensland, Brisbane, Queensland 4072, Australia
10. Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy
11. School of Ocean and Earth Science, University of Southampton, Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, UK
12. Byrd Polar Research Centre and Department of Geological Sciences, The Ohio State University, Columbus, Ohio 43210, USA
13. British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 OET, UK
14. Fysisch Geografisch en Bodemkundig Laboratorium, University of Amsterdam, Nieuwe Prinsengracht 130, 1018 VZ Amsterdam, The Netherlands
15. New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801, USA
16. Alfred-Wegener-Institute, Postfach 12 01 81, 27516, Bremerhaven, Germany
17. Department of Geology and Environmental Geosciences, Northern Illinois University, De Kalb, Illinois 60115, USA
18. Dipartimento di Scienze della Terra, Universitá degli Studi di Siena, Via del Laterino 8, 53100, Siena, Italy
19. Department of Geology, University of California, Davis, California 95616, USA
20. Dipartimento di Scienza della Terra, Universitá degli Studi di Parma, Parco Area Scienze 157A, 43100 Parma, Italy
21. Deceased.
22. Present addresses:RWE-DEA AG, Ueberseering 40 22297 Hamburg, Germany (C.J.B.); Agip Kazachstan North Caspian Operating Company, Raamweg 26, 2596 HL, The Hague, The Netherlands (M.C.); Department of Geography, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (J.v.d.M.).

Correspondence to: Tim R. Naish¹ Correspondence and requests for materials should be addressed to T.N. (e-mail: Email: t.naish@gns.cri.nz).

Between 34 and 15 million years (Myr) ago, when planetary temperatures were 3–4 °C warmer than at present and atmospheric CO₂ concentrations were twice as high as today¹, the Antarctic ice sheets may have been unstable^{2, 3, 4, 5, 6, 7}. Oxygen isotope records from deep-sea sediment cores suggest that during this time fluctuations in global temperatures and high-latitude continental ice volumes were influenced by orbital cycles^{8, 9, 10}. But it has hitherto not been possible to calibrate the inferred changes in ice volume with direct evidence for oscillations of the Antarctic ice sheets¹¹. Here we present sediment data from shallow marine cores in the western Ross Sea that exhibit well dated cyclic variations, and which link the extent of the East Antarctic ice sheet directly to orbital cycles during the Oligocene/Miocene transition (24.1–23.7 Myr ago). Three rapidly deposited glacimarine sequences are constrained to a period of less than 450 kyr by our age model, suggesting that orbital influences at the frequencies of obliquity (40 kyr) and eccentricity (125 kyr) controlled the oscillations of the ice margin at that time. An erosional hiatus covering 250 kyr provides direct evidence for a major episode of global cooling and ice-sheet expansion about 23.7 Myr ago, which had previously been inferred from oxygen isotope data (Mi1 event⁵).