We report on the scattering and excitation mechanisms of the terrestrial exospheric H I 1216-¿ and He I 584-¿ airglow emissions by comparing simulations from a radiative transfer model with spectroscopic measurements from an Earth-orbiting satellite. The purpose of these comparisons are twofold: to assess the sensitivity of the input parameters to the model results and to test the applicability of the model to airglow analysis. The model incorporates a spherically oriented atmosphere to account for the extended scale heights of the exospheric scatterers as well as to properly mimic scattering across the terminator region from the dayside to the nightside hemispheres. Spectroscopic Lyman &agr; and He I 584-¿ data were obtained by the STP78-1 satellite that circumnavigated the Earth in a noon/midnight orbit at an altitude of 600 km. The ''best fit'' analysis of the Lyman &agr; data acquired on March 25, 1979, requires scaling the hydrogen density distribution obtained from the MSIS-90 (Hedin, 1991) atmospheric model by 45-50%, the exospheric temperature by 90-100%, and the Lyman &agr; solar flux predicted by EUV91 model (Tobiska, 1991) by 1.9-2.0. Similar analysis of the He I 584-¿ data acquired on March 5, 1979, requires scaling the helium density distribution obtained from the MSIS-90- (Hedin, 1991) atmospheric model by 60--80% and the exospheric temperature by 105--115% while using a line center 584-¿ solar flux of 1.44¿1010 photons cm-2 s-1 ¿-1. ¿ American Geophysical Union 1995.