In this contribution results on self-organized patterns formed during low energy Xe+ ion beam erosion on Si and Ge surfaces are presented. It was found that the evolution of surface patterns depends on ion incidence angle, erosion time, and ion energy. In the case without sample rotation ripple patterns form on the Si and Ge surfaces with a wavelength lambda < 100 nm, for ion energies E-ion <= 2000 eV at near normal ion incidence (alpha(ion) similar to 5 degrees) and at room temperature. The experimental results of a decreasing ripple wavelength with ion incidence angle on Si coincide with the Bradley-Harper [J. Vac. Sci. Technol. A 6, 2390(1988).] theory of ripple formation. While the independency of lambda from the ion flux suggests that thermally activated surface diffusion can be ruled out as the dominant relaxation mechanism. Experiments reveal that the wavelength of ripples increases with ion energy. With sample rotation at 75 degrees ion incidence angle dot patterns form on the surface with a mean size X < 50 nm. (c) 2006 American Vacuum Society.