We use a time-dependent ice-cap model to predict the pattern of growth and decay of the Patagonian ice cap during a simulated glacial cycle. The purpose is to illuminate the internal system dynamics and identity thresholds of stability related to the underlying topography. This is a necessary step if former ice-cap behaviour is to be linked to climatic change. The model, which is fully described elsewhere, portrays ice extent and surface altitude at intervals of 1000–5000 years. The modelling suggests that there are two stable ice-cap states largely influenced by topography, namely, the present distribution of upland ice fields and the long, linear ice cap along the Andes as represented by the Last Glacial Maximum. Both states can coexist in equilibrium with a climate similar to that of the present day. There is a third, larger variable state in which a more extensive ice cap extends into the adjacent plains, as occurred during early Quaternary glaciations. Warmer and/or drier conditions are required to remove all these ice caps. There are five ice centres during ice-cap growth.