Coupled climate models are prone to “drift” (i.e., long-term unforced trends in state variables) due to incomplete spin-up and non-closure of the global mass and energy budgets. This work assesses model drift and the associated conservation of mass, energy and salt in the CMIP6 ensemble. For most models, drift in globally integrated ocean heat content represents a non-trivial fraction of historical trends. Model drift tends to be even larger in net top-of-the-atmosphere radiation, indicating a loss (or “leakage”) of heat in the coupled climate system. While this leakage is largest in the atmosphere (a known problem in coupled models), the CMIP6 oceans also gain or lose energy relative to the cumulative surface heat flux. Drift in ocean mass is also non-trivial when compared to historical sea level trends and is not conserved when compared to the cumulative surface freshwater flux. The magnitude of drift in the CMIP6 ensemble does not represent an improvement over CMIP5, but critically the closure of global mass and energy budgets after drift removal has improved.