Two global glaciations occurred during the Neoproterozoic. Snowball Earth theory posits that these were terminated after millions of years of frigidity when initial warming from rising atmospheric CO2 concentrations was amplified by the reduction of ice cover and hence a reduction in planetary albedo1, 2. This scenario implies that most of the geological record of ice cover was deposited in a brief period of melt-back3. However, deposits in low palaeo-latitudes show evidence of glacial–interglacial cycles4, 5, 6. Here we analyse the sedimentology and oxygen and sulphur isotopic signatures of Marinoan Snowball glaciation deposits from Svalbard, in the Norwegian High Arctic. The deposits preserve a record of oscillations in glacier extent and hydrologic conditions under uniformly high atmospheric CO2 concentrations. We use simulations from a coupled three-dimensional ice sheet and atmospheric general circulation model to show that such oscillations can be explained by orbital forcing in the late stages of a Snowball glaciation. The simulations suggest that while atmospheric CO2 concentrations were rising, but not yet at the threshold required for complete melt-back, the ice sheets would have been sensitive to orbital forcing. We conclude that a similar dynamic can potentially explain the complex successions observed at other localities. Document embargo 24/02/2016.