We present a numerical eigenmode analysis of an intermediate El Ni¿o--Southern Oscillation (ENSO) model which is driven by present-day observed background conditions as well as by simulated background conditions for the Last Glacial Maximum (LGM) about 21,000 years ago. The background conditions are obtained from two LGM simulations which were performed with the National Center for Atmospheric Research climate system model (CSM1.4) and an Earth system model of intermediate complexity (ECBilt-CLIO). Our analysis clearly shows that the leading present-day unstable recharge-discharge mode changes its stability as well as its frequency during LGM conditions. Simulated LGM background conditions were favorable to support large-amplitude self-sustained interannual ENSO variations in the tropical Pacific. Our analysis indicates that off-equatorial climate conditions as well as a shoaling of the thermocline play a crucial role in amplifying the LGM ENSO mode.