Phase 6 of the Coupled‐Model Intercomparison Project (CMIP6) is the first in which a significant number of models include a well‐resolved stratosphere. Changes in equatorial stratospheric variability in historical and Shared Socioeconomic Pathways (SSPs) scenario simulations are investigated in 10 models with realistic quasi‐biennial oscillations (QBO). All project a weakening of the QBO throughout the stratosphere for SSP370 and SSP585 scenarios and for 1960 to 2010. The weakening is strongest in the lower stratosphere, ranging from urn:x-wiley:grl:media:grl60277:grl60277-math-0001% to urn:x-wiley:grl:media:grl60277:grl60277-math-0002 % to urn:x-wiley:grl:media:grl60277:grl60277-math-0003% per decade at 50 hPa for SSP585, SSP370, and historical simulations, respectively. At 20 hPa a weakening of both westward and eastward phases contributes though the weakening eastward phase is only seen in 7 of the 10 models. Similar robust weakening occurs for the temperature QBO, but only from 30 hPa upward. In both scenarios the QBO period decreases in 7 of the 10 models.