A rigorous error analysis is applied to the retrieval of chlorine monoxide (ClO), ozone (O3), and water vapor (H2O) profiles from millimeter wave spectra measured with a limb sounding instrument at 204, 184, and 183 GHz. The effect of different height resolutions on the accuracy and precision is studied. The nature of the different error sources and their contributions to the total error are discussed. A quantitative analysis for a specific limb sounding experiment, the MAS on the ATLAS spacelab shuttle program, is presented. The accuracy of the profiles to be retrieved is 30% for ClO around 35 km (for an altitude resolution of 5 km and an integration time of 200 s per tangent height). O3 can be retrieved at an accuracy of 5 to 9% between 18 and 60 km (3 km; 1--100 s, depending on height). H2O can be retrieved at an accuracy of 4 to 9% between 20 and 75 km (3 km; 1--100 s). For O3, measurements at a resolution of 1 km are possible between 18 and 50 km, for H2O between 20 and 60 km. ¿American Geophysical Union 1993