While observations suggest a long-term expansion of the Oxygen Minimum Zone (OMZ) in the South Eastern Pacific (SEP), it also exhibits a large interannual to decadal variability in its upper and lower limits. The uncertainty of the fate of the SEP OMZ in a warmer climate as simulated by Earth system models also questions to which extent natural variability in the OMZ can obscure the detection of externally forced trends. Here we analyze long-term simulations from a hierarchy of models of the OMZ off Peru and Chile and show that a significant share of the variability is not linearly related to climate modes (including ENSO), suggesting that it originates from internal dynamics associated to both local non-linear physical and biogeochemical p...