In this paper, a new type of spectral filter mirrors for extreme ultraviolet radiation based on DLC/Si multilayer coatings is presented (DLC - diamond-like carbon). The coating is nearly transparent for infrared radiation (IR) of lambda=10.6 nm but highly reflective at lambda=13.5 nm (EUV). We deposited DLC/Si multilayers by ion beam sputter deposition with 40 and 60 periods exhibiting maximum EUV reflectances of about R(sub max)=43 % and R(sub max)=50 %, respectively. Combining IR antireflective and EUV reflective coatings, first prototype mirrors have been fabricated with an EUV reflectance of about 42.5 % and an IR reflectance of about 4.4 % at the same time. Investigations on the thermal behavior of the multilayer stack and the cleaning properties for tin contaminated mirror surfaces have been carried out. Excellent stabilities of EUV peak position and reflectance values have been found using annealing temperatures of up to 700 degrees C. Furthermore, several cycles of Sn etching under H(sub 2) reactive conditions have been applied to the mirrors without significant changes of the filter performance