A method for the simultaneous determination of rubidium, caesium, barium and eight rare earth elements in rocks by neutron-activation analysis is described. The method is suitable for use with samples with particularly low abundances of the elements concerned. After fusion with alkali and determination of rubidium and caesium in the supernatant liquid, the hydroxide fraction is carried through an anion-exchange step in chloride media and extracted with tri-n-butyl phosphate in order to remove interfering nuclides. Subsequently, barium, strontium and the rare earths are separated into three groups by mixed-solvent anion exchange.The method is shown to be suitable for application to ultramafic rocks. Results for rubidium, caesium, lutetium, ytterbium, terbium, europium, samarium, neodymium, cerium and lanthanum in dunite DTS-1 are presented. Granite (G-2) was also analysed in order to assess the accuracy of the method.