[en] The interaction of rare gas clusters with short-wavelength radiation of free-electron lasers (FELs) has been studied extensively over the last decade by means of electron and ion time-of-flight spectroscopy. This thesis describes the design and construction of a fluorescence spectrometer for the extreme ultraviolet (XUV) spectral range and discusses the cluster experiments performed at FLASH, the Free-electron LAser in Hamburg. Fluorescence of xenon and of argon clusters was studied, both in dependence on the FEL pulse intensity and on the cluster size. The FEL wavelength was set to the giant 4d-resonance of xenon at 13.5 nm and the FEL pulse intensity reached peak values of 2.7.10¹⁵ W/cm². For xenon clusters, charge states of at least 11+ were identified. For argon, charge states up to 7+ were detected. The cluster-size dependent study revealed a decrease of the fluorescence yield per atom with increasing cluster size. This decrease is explained with the help of a geometric model. It assumes that virtually the entire fluorescence yield stems from shells of ions on the cluster surface, whereas ions in the cluster core predominantly recombine non-radiatively with electrons. However, the detailed analysis of fluorescence spectra from clusters consisting of a core of Xe atoms and a surrounding shell of argon atoms shows that, in fact, a small fraction of the fluorescence signal comes from Xe ions in the cluster core. Interestingly, these ions are as highly charged as the ions in the shells of a pure Xe cluster. This result goes beyond the current understanding of charge and energy transfer processes in these systems and points toward the observation of ultrafast charging dynamics in a time window where mass spectrometry is inherently blind. (orig.)