The processes occurring in the tropical tropopause layer (TTL) are of great importance for stratosphere–troposphere exchanges and the variability of the Earth's climate. Previous studies demonstrated the increasing ability of atmospheric general circulation models (AGCMs) in simulating the TTL, depending on factors such as the horizontal and vertical resolution, with the major role for physical parametrizations. In this work we assess the mean state and variability of the tropical upper troposphere and lower stratosphere simulated by 13 AGCMs of the Stratosphere–troposphere Processes And their Role in Climate Quasi-Biennial Oscillation initiative (QBOi) for the historical period. As these models internally generate quasi-biennial oscillations (QBOs) of the stratospheric zonal wind, we can analyse the simulated QBO influence on the TTL on interannual time-scales. We find that model biases in temperature near the tropopause are strongly related to water vapour concentrations in the lower stratosphere. A source of intermodel spread derives from stratospheric aerosols, as the responses to eruptions differ between those models prescribing volcanic aerosol forcing. The QBO influence on the thermal structure is generally realistic in the equatorial region, but the subtropical response is weak compared with the reanalysis. This is associated with a limited downward penetration of QBO winds, generally smaller QBO meridional widths, and weaker temperature anomalies, which disappear above the tropopause for most models. We discuss the QBO impacts on tropopause pressure and precipitation, characterized by large uncertainties due to the small signal in the observational records and sampling uncertainty. Realistic QBO connection with the troposphere in some models suggests that the underlying physical processes can be correctly simulated. Overall, we find that the QBOi models have limited ability to reproduce the observed modulation of the TTL processes, which is consistent with biases in the vertical and latitudinal extent of the simulated QBOs degrading this connection.