El Niño–Southern Oscillation (ENSO) is a major source for teleconnections, including towards the tropical North Atlantic (TNA) region, whereby TNA sea surface temperatures (SSTs) are positively correlated with ENSO in boreal spring following an ENSO event. However, the Pacific–Atlantic connection can be impacted by different ENSO characteristics, such as the amplitude, location, and timing of Pacific SST anomalies (SSTAs). Indeed, the TNA SSTAs may respond nonlinearly to strong and extreme El Niño events. However, observational data for the number of extreme ENSO events remain limited, restricting our ability to investigate the influence of observed extreme ENSO events. To overcome this issue and to further evaluate the nonlinearity of the TNA SSTA response, two coupled climate models are used, namely the Community Earth System Model version 1 – Whole Atmosphere Community Climate Model (CESM-WACCM) and the Flexible Ocean and Climate Infrastructure version 1 (FOCI). In both models the TNA SSTAs respond linearly to ENSO during extreme El Niño events but nonlinearly to extreme La Niña events for CESM-WACCM. We investigate differences by using indices for all major mechanisms that connect ENSO to the TNA and compare them with reanalysis. CESM-WACCM and FOCI overall represent the teleconnection well, including that the tropical and extratropical pathways are similar to observations. Our results also show that a large portion of the nonlinearity during La Niña is explained by the interaction between Pacific SSTAs and the overlying upper-level divergence.