Abstract Advanced numerical climate models are known to exhibit biases in simulating some features of El Niño–Southern Oscillation (ENSO), which is a key mode of interannual climate variability. In this study we analyze how two fundamental features of observed ENSO – asymmetry between hot and cold states and phase-locking to the annual cycle – are reflected in two different versions of the INMCM Earth system model (state-of-the-art Earth system model participating in the Coupled Model Intercomparison Project). We identify the above ENSO features using the conventional empirical orthogonal functions (EOF) analysis, which is applied to both observed and simulated upper ocean heat content (OHC) data in the tropical Pacific. We obtain that the observed tropical Pacific OHC variability is described well by two leading EOF-modes, which roughly reflect the fundamental recharge-discharge mechanism of ENSO. These modes exhibit strong seasonal cycles associated with ENSO phase locking while the revealed nonlinear dependencies between amplitudes of these cycles reflect ENSO asymmetry.We also assess and compare the predictability of observed and simulated ENSO based on linear inverse modelling. We find that the improved INMCM6 model has significant benefits in simulating described features of observed ENSO as compared with the previous INMCM5 model. The improvements of the INMCM6 model providing such benefits are discussed. We argue that proper cloud parameterization scheme is crucial for accurate simulation of ENSO dynamics with numerical climate models.