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The Quasi‐Biennial Oscillation initiative (QBOi) is a model intercomparison programme that specifically targets simulation of the QBO in current global climate models. Eleven of the models or model versions that participated in a QBOi intercomparison study have upper boundaries in or above the mesosphere and therefore simulate the region where the stratopause semiannual oscillation (SAO) is the dominant mode of variability of zonal winds in the tropical upper stratosphere. Comparisons of the SAO simulations in these models are presented here. These show that the model simulations of the amplitudes and phases of the SAO in zonal‐mean zonal wind near the stratopause agree well with the information derived from available observations. However, most of the models simulate time‐average zonal winds that are more westward than determined from observations, in some cases by several tens of m·s$^{–1}$. Validation of wave activity in the models is hampered by the limited observations of tropical waves in the upper stratosphere but suggests a deficit of eastward forcing either by large‐scale waves, such as Kelvin waves, or by gravity waves.