In this study, using the Bjerknes stability (BJ) index analysis, we estimate the overall linear El Niño-Southern Oscillation (ENSO) stability and the relative contribution of positive feedbacks and damping processes to the stability in historical simulations of Coupled Model Intercomparison Project Phase 5 (CMIP5) models. When compared with CMIP3 models, the ENSO amplitudes and the ENSO stability as estimated by the BJ index in the CMIP5 models are more converged around the observed, estimated from the atmosphere and ocean reanalysis data sets. The reduced diversity among models in the simulated ENSO stability can be partly attributed to the reduced spread of the thermocline feedback and Ekman feedback terms among the models. However, a systematic bias persists from CMIP3 to CMIP5. In other words, the majority of the CMIP5 models analyzed in this study still underestimate the zonal advective feedback, thermocline feedback and thermodynamic damping terms, when compared with those estimated from reanalysis. This discrepancy turns out to be related with a cold tongue bias in coupled models that causes a weaker atmospheric thermodynamical response to sea surface temperature changes and a weaker oceanic response (zonal currents and zonal thermocline slope) to wind changes. © 2013 Springer-Verlag Berlin Heidelberg.