A numerical 2D-simulation of the transformation of a contrail in its vortex phase to a cirrus-like cloud during the dispersion phase has been performed using a model that handles both wake dynamics and ice microphysics. The contrail is located in an environment characterized by measured profiles of wind and temperature. The ambient humidity at cruise level slightly exceeds ice-saturation. The thermal structure of the atmosphere causes a strong vertical growth of the contrail cloud, even into a dry layer, until a stably stratified layer is reached. Thereafter the cloud expands mainly horizontally and after 30 min it eventually disappears because of entrainment of dry ambient air. ¿ 1998 American Geophysical Union