We describe a new inversion algorithm developed for the retrieval of atmospheric constituents from Stratospheric Aerosol and Gas Experiment III (SAGE III) solar occultation measurements. The methodology differs from the operational (NASA) algorithm in several important ways. Our algorithm takes account of the finite altitude and spectral resolution of the measurements by integrating over the viewing window spectrally and spatially. We solve the problem nonlinearly by using optimal estimation theory, and we use an aerosol parameterization scheme based on eigenvectors derived from existing empirical and modeled information about their microphysical properties. The first four of these eigenvectors are employed in the retrieval algorithm to describe the spectral variation of the aerosol extinction. We retrieve ozone and nitrogen dioxide number densities and aerosol extinction from transmission measurements at 41 channels from 0.29 to 1.55 ¿m. In this paper we describe the results of the gas retrievals. Numerical simulations test the accuracy of the scheme, and subsequent retrievals from SAGE III transmission data for the period between May and October 2002 produce profiles of O3 and NO2. Comparisons of the O3 and NO2 profiles with those obtained using the SAGE III operational algorithm and with those from independent measurements made by satellites, ozonesondes, and lidar indicate agreement in ozone measurements in the middle and upper stratosphere significantly closer than the natural variability and agreement in the lower stratosphere and upper troposphere approximately equal to the natural variability.