On the basis of data on the slant-path atmospheric transmittance measured with the Ozon-Mir instrumentation of the Mir space station, the vertical profiles of the volume aerosol extinction coefficient (VAEC) at 0.4, 0.7, and 1 μm were obtained in the height range from 13-18 to 35-40 km. The VAEC inherent error at a wavelength of 1 μm for the lower boundary of the height range under study is 5-8% and increases as the wavelength decreases and the height increases, ranging at all three wavelengths up to 50-100% for heights of 35-40 km. The data of the measurements performed from December 1996 to February 1997 are in the best quantitative accordance with the aerosol model of the background stratosphere LOWTRAN-7. The other available models [18, 19, 21] of a slightly turbid stratosphere give VAEC values that are 1.5-5 times lower than the measured ones. A comparison of the retrieved profiles with the mean VAEC profiles obtained from the SAGE-II data is performed. The Ozon-Mir and SAGE-II data on aerosol extinction coefficients are in good agreement. The differences between them are close to the VAEC natural variability, although the Ozon-Mir values are somewhat greater than the SAGE-II mean values obtained in the corresponding months and latitudinal zones. A comparison between the Ozon-Mir and SAGE-I Ångström coefficient values shows that these values are in satisfactory agreement. The SAGE-I and Ozon-Mir measurements under consideration were performed during the periods characterized by the background stratospheric aerosol content even if significantly separated in time.