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The upper 1200 m of pre-Pliocene sediment recovered by Cape Roberts Project (CRP) drilling off the Victoria Land coast of Antarctica between 1997-1999 has been subdivided into 54 unconformity-bound stratigraphic sequences, spanning the period c. 32 to 17 Ma. The sequences are recognised on the basis of the cyclical vertical stacking of their constituent lithofacies, which are enclosed by erosion surfaces produced during the grounding of the advancing ice margin onto the sea floor. Each sequence represents deposition in a range of offshore shelf to coastal glacimarine sedimentary environments during oscillations in the ice margin across the Western Ross Sea shelf, and coeval fluctuations in water depth. This paper applies spectral analysis techniques to depth- and time-series of sediment grain size (500 samples) for intervals of the core with adequate chronological data. Time series analysis of 0.5-1.0m-spaced grainsize data spanning sequences 9-11 (CRP-2/2A) and sequences 1-7 (CRP-3) suggests that the length of individual sequences correspond to Milankovitch frequencies, probably 41 k.y., but possibly as low as 100 k.y. Higher frequency periodic components at 23 k.y. (orbital precession) and 15-10 k.y. (sub-orbital) are recognised at the intrasequence-scale, and may represent climatic cycles akin to the ice rafting episodes described in the North Atlantic Ocean during the Quaternary. The cyclicity recorded by glacimarine sequences in CRP core provides direct evidence from the periphery of Antarctica for orbital oscillations in the size of the Oligocene-Early Miocene East Antarctic Ice Sheet.