Scientific studies of the major environmental questions of global warming and ozone depletion require global data sets of atmospheric constituents with relevant temporal and spatial resolution. In this paper, global number density profiles of O3 and NO2 are retrieved from Odin Optical Spectrograph and Infrared Imager System (Odin/OSIRIS) limb-scattered sunlight measurements, using the maximum a posteriori estimator. Differential optical absorption spectroscopy is applied to OSIRIS radiances as an intermediate step, using the wavelength windows 571--617 nm for O3 and 435--451 nm for NO2. The method is computationally efficient for processing OSIRIS data on an operational basis. Results show that a 2--3 km height resolution is generally achievable between about 12 km and 45 km for O3 with an estimated accuracy of 13% at the peak and between about 15 km and 40 km for NO2 with an estimated accuracy of 10% at the peak. First validations of the retrieved data indicate a good agreement both with other retrieval techniques applied to OSIRIS measurements and with the results of other instruments. Once the validation has reached a confident level, the retrieved data will be used to study important stratospheric processes relevant to global environmental problems. The unique NO2 data set will be of particular interest for studies of nitrogen chemistry in the middle atmosphere.