A method is described for the determination of traces of rare earths using energy-dispersive x-ray fluorescence spectrometry (EDXRF) after preconcentration of their quinolin-8-ol complexes on activated carbon. Various parameters that influence the adsorptive preconcentration of rare earths on activated carbon, viz., pH, amounts of activated carbon and quinolin-8-ol, time of stirring and aqueous phase volume, were systematically studied. A numerical method based on a simple least-squares procedure using a fifth-order polynomial with 25 consecutive values was developed for smoothing and differentiation of EDXRF data which were previously digitized and averaged. First-order derivative EDXRF in conjunction with adsorptive preconcentration of activated carbon enables down to 10 ng ml-1 of each rare earth element to be determined. © 1991.