<p>Multi-year La Niña events are characterized by their prolonged duration and more severe climate effects. Based on historical experiment data from the Coupled Model Intercomparison Project Phase 6 (CMIP6) simulations, a detailed analysis for the simulations of multi-year La Niña events from state-of-the-art models is conducted. According to their performance in terms of the occurrence frequency and seasonal phase-locking of multi-year La Niña events, the CMIP6 models are categorized into two groups: Group A and Group B. Group A models can simulate the double-dip cooling evolution with the cooling relaxation occurring between the two cooling dips. However, Group B models can only simulate a single persisting cooling, failing to reproduce the second-year (year01) cooling dip without cooling relaxation during the evolution. Further seasonal transition analysis reveals that Group A models exhibit a coherent relationship among sea surface temperature (SST) rewarming, decaying wind stress divergence, and subsurface warming in the summer of year01. Conversely, Group B models fail to show the SST anomaly cooling relaxation and the formation of wind stress anomaly convergence centers. Although subsurface rewarming also appears in Group B models, there are significant biases in both horizontal and vertical positions. Mixed-layer heat budget analyses indicate that thermal damping, zonal advection, and thermocline feedback all contribute to the failure of cooling relaxation in Group B, with thermocline feedback playing the most significant role, accounting for 46.4% of the total negative contribution in April of year01. Further research shows that strong upwelling working together with colder subsurface temperature leads to overestimated thermocline feedback in Group B models.</p>