We investigated single shot damage of Mo/Si multilayer coatings exposed to the intense fs XUV radiation at the Free-electron LASer facility in Hamburg - FLASH. The interaction process was studied in situ by XUV reflectometry, time resolved optical microscopy, and “post-mortem” by interference-polarizing optical microscopy (with Nomarski contrast), atomic force microscopy, and scanning transmission electron microcopy. An ultrafast molybdenum silicide formation due to enhanced atomic diffusion in melted silicon has been determined to be the key process in the damage mechanism. The influence of the energy diffusion on the damage process was estimated. The results are of significance for the design of multilayer optics for a new generation of pulsed (from atto- to nanosecond) XUV sources.