A portable isotope-excited X-ray fluorescence system, incorporating balanced filters, was tested on outcrops of rare-element-bearing Precambrian alkaline rocks of the Ilimaussaq intrusion, S. Greenland. Mineralizations examined included sheared lavas and dikes containing disseminated murmanite, peralkaline syenites-naujaite, kakortokite, and lujavrite containing one or more of the minerals, eudialyte, monazite, steenstrupine, and rinkite, and hydrothermal veins with pyrochlore and lueshite (igdloite). Calibration curves for Zr, Nb, and La + Ce were obtained from regression analyses of field count rates versus wet chemical, mass spectrometric, and X-ray spectrographic assays of chip samples and sawed rock slabs. Detection limits, based on the regression analyses' 95% confidence intervals, were 0.44% for Zr, 0.15% for Nb, and 0.17% for La + Ce. Precision, estimated from difference count rates, was less than 15% (relative error) for Zr and Nb, and between 15 and 30% for La + Ce. Accuracy, based on the regression analyses, was about 0.15% for the elements measured. Traverses across terranes containing varying amounts of these elements showed that the system detects and analyses disseminated mineralizations of possible economic value. Zr contents ranged from below the detection limit in steenstrupine lujavrites and analcime veins to 4.7% in eudialyterich kakortokite, Nb varied from below the detection limit in steenstrupine lujavrites and white and black kakortokites to 0.51% in pyrochlore-bearing analcime veins, and La + Ce from 0.24% in black kakortokite to 1.21% in steenstrupine-rich fine-grained lujavrite.