Theoretical profiles of cosmogenic 7Be in the atmosphere above 100 km were computed in an effort to explain unexpectedly high accumulations of this radionuclide found on the leading surfaces of the Long Duration Exposure Facility (LDEF) spacecraft. Our diffusion calculations suggest that gravitational fractionation is suffient to explain most, and possibly all, of the observed 7Be enrichment at the recovery altitude of the spacecraft, provided only that the nuclide exists at and above the turbopause predominantly in the form of free atoms. Upward diffusion of 7Be atoms through the turbopause appears to occur rapidly enough to largely offset losses at higher altutides due to radioactive decay. The same model is used to compute cosmogenic 10Be profiles in order to predict the probable outcome of planned measurements of 10Be accumulations of LDEF surfaces. ¿ American Geophysical Union 1991