Fluorine or a fluorine compound is subjected to a reaction with a spent oxide fuel to produce fluorides of uranium and plutonium, and the fluorides are recovered using a difference in volatility behavior. The spent oxide fuel is subjected to a reaction with an HF gas, whereby uranium, plutonium and most impurities are converted into solid fluorides having low valences or remained as oxides to inhibit volatilization thereof, and then in an F.sub.2 fluorination step, the HF fluorination product is subjected to a reaction with a fluorine gas in two stages: one at a low temperature and the other at a high temperature, whereby a certain amount of gaseous uranium and volatile impurities are separated with plutonium kept in a solid form in the first stage, and mixed fluorides of remaining uranium and plutonium are fluorinated into hexafluorides at the same time in the second stage. By such a reprocessing method, plutonium enrichment can be adjusted, uranium and plutonium can be purified, and steps are simplified as well. In addition, reactors are hard to be corroded or deteriorated.