Cesium and strontium are extracted from aqueous acidic radioactive waste containing rare earth elements, technetium and actinides, by contacting the waste with a composition of a complex organoboron compound and polyethylene glycol in an organofluorine diluent mixture. In a preferred embodiment the complex organoboron compound is chlorinated cobalt dicarbollide, the polyethylene glycol has the formula RC.sub.6 H.sub.4 (OCH.sub.2 CH.sub.2).sub.n OH, and the organofluorine diluent is a mixture of bis-tetrafluoropropyl ether of diethylene glycol with at least one of bis-tetrafluoropropyl ether of ethylene glycol and bis-tetrafluoropropyl formal. The rare earths, technetium and the actinides (especially uranium, plutonium and americium), are extracted from the aqueous phase using a phosphine oxide in a hydrocarbon diluent, and reextracted from the resulting organic phase into an aqueous phase by using a suitable strip reagent.