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Experimental results are presented obtained with a cryogenically cooled high-resolution X-ray spectrometer based on a 141 × 141 µm Nb-Al-Al2O3-Al-Nb superconducting tunnel junction (STJ) detector in an SR-XRF demonstration experiment. STJ detectors can operate at count rates approaching those of semiconductor detectors while still providing a significantly better energy resolution for soft X-rays. By measuring fluorescence X-rays from samples containing transition metals and low-Z elements, an FWHM energy resolution of 6-15 eV for X-rays in the energy range 180-1100 eV has been obtained. The results show that, in the near future, STJ detectors may prove very useful in XRF and microanalysis applications.