Under extreme ultraviolet (EUV) exposure, the surfaces of the, imaging optics and mask, which are coated with a Mo/Si multilayer, become contaminated with organic compounds. Thus, an efficient method of removing carbon contamination from masks and the imaging optics is required. Then, we propose two methods as a removal method of contamination: one is in situ cleaning method without heating a sample by synchrotron radiation irradiation that is mainly targeted at the imaging optics, and another is cleaning method without heating a sample using by 172 nm light irradiation that is targeted at an EUV lithography finished mask. For in situ cleaning so called online cleaning, the contamination removal rate is 0.24 nm/min in the condition of O-2-rich-vacuum environment at a pressure of 5.0x10(-2) Pa and an electron beam current of 130 mA of 1.0. GeV electron storage ring. For offline cleaning using 172 nm light, the contamination removal rate is 2 nm/min in the O-2-rich-vacuum environment at the pressure of 2x10(-3) Pa. Both two methods restore the reflectivity of a Mo/Si multilayer to its original level without causing any surface damage. The effectiveness of both in situ and offline contamination removal are confirmed. (C) 2005 American Vacuum Society.