AbstractA new phenomenon on X-ray optics surfaces has been observed: the growth of nano-dots (40-55 nm diameter, 8-13 nm height, 9.4 dots µm-2 surface density) on the grazing-incidence mirror surface under irradiation by the free-electron laser (FEL) FLASH (5-45 nm wavelength, 3° grazing-incidence angle). With a model calculation it is shown that these nano-dots may occur during the growth of a contamination layer due to polymerization of incoming hydrocarbon molecules. The crucial factors responsible for the growth of nano-dots in the model are the incident peak intensity and the reflection angle of the beam. A reduction of the peak intensity (e.g. replacement of the FEL beam by synchrotron radiation) as well as a decrease of the incident angle by just 1° (from 3° to 2°) may result in the total disappearance of the nano-dots. The model calculations are compared with surface analysis of two FLASH mirrors.