A long-standing difficulty of climate models is to capture the annual cycle (AC) of eastern equatorial Pacific (EEP) sea surface temperature (SST). In this study, we first examine the EEP SST AC in a set of integrations of the coupled Kiel Climate Model, in which only atmosphere model resolution differs. When employing coarse horizontal and vertical atmospheric resolution, significant biases in the EEP SST AC are observed. These are reflected in an erroneous timing of the cold tongue’s onset and termination as well as in an underestimation of the boreal spring warming amplitude. A large portion of these biases are linked to a wrong simulation of zonal surface winds, which can be traced back to precipitation biases on both sides of the equator and an erroneous low-level atmospheric circulation over land. Part of the SST biases also is related to shortwave radiation biases related to cloud cover biases. Both wind and cloud cover biases are inherent to the atmospheric component, as shown by companion uncoupled atmosphere model integrations forced by observed SSTs. Enhancing atmosphere model resolution, horizontal and vertical, markedly reduces zonal wind and cloud cover biases in coupled as well as uncoupled mode and generally improves simulation of the EEP SST AC. Enhanced atmospheric resolution reduces convection biases and improves simulation of surface winds over land. Analysis of a subset of models from the Coupled Model Intercomparison Project phase 5 (CMIP5) reveals that in these models, very similar mechanisms are at work in driving EEP SST AC biases.