Abstract. It is commonly accepted that the variations of Earth's orbit and obliquity control the timing of Pleistocene glacial–interglacial cycles. Evidence comes from power spectrum analysis of palaeoclimate records and from inspection of the timing of glacial and deglacial transitions. However, we do not know how tight this control is. Is it, for example, conceivable that random climatic fluctuations could cause a delay in deglaciation, bad enough to skip a full precession or obliquity cycle and subsequently modify the sequence of ice ages?

To address this question, seven previously published conceptual models of ice ages are analysed by reference to the notion of generalised synchronisation. Insight is being gained by comparing the effects of the astronomical forcing with idealised forcings composed of only one or two periodic components. In general, the richness of the astronomical forcing allows for synchronisation over a wider range of parameters, compared to periodic forcing. Hence, glacial cycles may conceivably have remained paced by the astronomical forcing throughout the Pleistocene.

However, all the models examined here show regimes of strong structural dependence on parameters. This means that small variations in parameters or random fluctuations may cause significant shifts in the succession of ice ages. Whether the actual system actually resides in such a regime depends on the amplitude of the effects associated with the astronomical forcing, which significantly differ across the different models studied here. The possibility of synchronisation on eccentricity is also discussed and it is shown that a high Rayleigh number on eccentricity, as recently found in observations, is no guarantee of reliable synchronisation.