Simultaneous measurements of disk-viewing OI 135.6 nm and N2 Lyman-Birge-Hopfield (LBH) dayglow can be used to monitor the solar EUV flux QEUV and the column abundance of thermospheric O relative to N2 (O/N2). We report on a study that quantifies the relationships between these emissions and the above parameters. Emission is considered from 134.5 to 139.0 nm (designated 135.6 nm) and from 155.0 to 170.0 nm (designated as LBH) at a resolution of 3.6 nm. The intervals and resolution were chosen for analysis of satellite dayglow data to be reported in the companion paper by Evans et al. (this issue). The first interval is dominated by OI 135.6 nm with minor contributions from LBH 135.4 and 138.3 nm. The second interval contains only LBH. An important finding is that 135.6/LBH is essentially independent of the solar EUV spectrum from low to high activity based on using the Hinteregger formulation for characterizing spectral changes with solar activity. Given this behavior in 135.6/LBH, one can then unambiguously interpret changes in this ratio in terms of changes in O/N2. Model results show that the relationship between O/N2 and 135.6/LBH is essentially independent of model atmosphere. Given either 135.6/LBH or O/N2, QEUV can then be obtained directly from the absolute intensity of either 135.6 nm or LBH. ¿ American Geophysical Union 1995