The ability to simulate atmospheric dispersion with models developed for applied use under stable atmospheric stability conditions is discussed. The paper is based on model simulations of three experimental data sets reported in the literature. The Hanford data set covered weakly stable conditions, the Prairie Grass experiments covered both weakly stable and very stable atmospheric conditions, and the Lillestrom experiment was carried out during very stable conditions. Simulations of these experiments reported in the literature for eight different models are discussed. Applied models based on the Gaussian plume model concept with the spread parameters described in terms of the Pasquill stability classification or Monin-Obukhov similarity relationships are used. Other model types are Lagrangian particle models which also are parameterized in terms of Monin-Obukhov similarity relationships. The applied models describe adequately the dispersion process in a weakly stable atmosphere, but fail during very stable atmospheric conditions. This suggests that Monin-Obukhov similarity theory is an adequate tool for the parameterization of the input parameters to atmospheric dispersion models during weakly stable conditions, but that more detailed parameterisations including other physical processes than those covered by the Monin-Obukhov theory should be developed for the very stable atmosphere.