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A prilled ammonium nitrate containing 2 to 5 percent by weight water obtained by prilling an aqueous solution of 93 to 98 percent by weight ammonium nitrate is dried by: lowering the drying temperature of the ammonium nitrate to a temperature less than the III-IV crystalline transition temperature of ammonium nitrate at least once when the water content of the prilled ammonium nitrate is 0.3 to 1.5 percent by weight in the drying step; further drying at a temperature higher than the III-IV transition temperature; and adding an anti-caking agent to the dried prilled ammonium nitrate. The dried, prilled ammonium nitrate obtained is useful as an ammonium nitrate fuel oil explosive.