The algorithm for determining spectral UVA (320--400 nm) and UVB (290--320 nm) flux in cloud-free conditions is discussed, including estimates of the various error sources (uncertainties in ground reflectivity, ozone amount, ozone profile shape, surface height, and aerosol attenuation). It is shown that the Brewer-measured spectral dependence of UV flux can be accurately reproduced using just total column ozone amount and the solar flux spectrum. The presence of aerosols tends to reduce the logarithm of the absolute UV flux linearly with aerosol optical depth. Using Brewer measurements of UV flux and aerosol optical depth on clear days at Toronto, the estimated slope falls in the range 0.2 to 0.3 (aerosol single-scattering albedo about 0.95). The Brewer measurements of UV flux can be reproduced using the aerosol model derived within uncertainties of the instrument calibration. We have applied the algorithm to the data collected by the total ozone mapping spectrometer (TOMS) instruments that have been flown by NASA since November 1978. It was demonstrated that in the absence of clouds and UV-absorbing aerosols, TOMS measurements of total column ozone and 380 nm (or 360 nm) radiances can be used in conjunction with a radiative transfer model to provide estimates of surface spectral flux to accuracies comparable to that of typical ground-based instruments. A newly developed technique using TOMS aerosol index data also allows estimation of UV flux transmission by strongly absorbing aerosols. The results indicate that over certain parts of the Earth, aerosols can reduce the UV flux at the surface by more than 50%. Therefore the most important need for reducing errors in TOMS-derived surface UVB spectra is to improve the understanding of UV aerosol attenuation. ¿ 1998 American Geophysical Union