The Hybrid K-Edge/K-XRF Densitometry (HKED) is the leading radiometric technique for the non-destructive assay of uranium and plutonium in nuclear safeguards samples and for process control in nuclear fuel reprocessing. It is based on X-ray transmission and X-ray fluorescence spectrometry. The Joint Research Centre (JRC) has organized an exercise to assess the capabilities of HKED spectrum processing algorithms and to identify areas for improvement. Within the exercise, the JRC distributed spectra recorded by HKED systems operated by the JRC to the international community of HKED users. The first set of spectra was distributed in May 2019 and another one in March 2020. These sets included spectra of well-characterized nuclear fuel reprocessing input solutions, and of dissolved uranium and MOX samples. The results of the spectrum analyses were better with the second set than with the first set, likely indicating improvements of the algorithms. All algorithms performed excellently with spectra of dissolved uranium and MOX pellets, and not as good with reprocessing input solutions. The reasons for this behavior need to be better understood and addressed in the algorithms. A third round of joint analysis, with a new set of spectra, is in preparation.