A new retrieval algorithm for the determination of aerosol properties using Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements based on nonlinear optimal estimation is presented. Using simulated MAX-DOAS measurements of the optical depth of the collision complex of oxygen (O4) as well as the variation of the intensity of diffuse skylight measured at different viewing directions and wavelengths, the capability of this measurement technique to derive the aerosol extinction profile as well as information on the phase function and single scattering albedo is demonstrated. The information content, vertical resolution and retrieval errors under various atmospheric conditions are discussed. Furthermore, it is demonstrated that the assumption of a smooth variation of the aerosol properties between successive measurements can be used to improve the quality of the retrieval by applying a Kalman smoother. The results of these model studies suggest that the achievable precision of MAX-DOAS measurements of the aerosol total optical depth is better than 0.01 and thus comparable with established methods of aerosol detection by Sun photometers (e.g., within the AERONET network) over a wide range of atmospheric conditions. Moreover, MAX-DOAS measurements contain information on the vertical profile of the aerosol extinction, and can be performed with relatively simple, robust and self-calibrating instruments.