An EUV light source for a projection exposure apparatus for EUV projection lithography includes a first electron beam device in the form of an electron beam supply device. The light source furthermore includes an EUV generation device supplied with an electron beam by the electron beam supply device. The light source furthermore includes a second electron beam device in the form of an electron beam disposal device which disposes of an electron beam in the beam path downstream of the EUV generation device. At least one of the electron beam devices on the one hand and the EUV generation device on the other hand are arranged in rooms which are situated one above the other and separated by a building ceiling. At least one electron beam passage is arranged in the building ceiling. This results in an electron beam-based EUV radiation source with the possibility of a manageable operational outlay.