Abstract: The invention relates to the field of separating rare earth elements by chromatography. The claimed method for separating lutetium and ytterbium from acidic solutions resulting from the recycling of irradiated ytterbium-176 targets is carried out using ion exchange chromatography. Ion sorption is performed on a sulphonic cation resin in copper or nickel form, and lutetium and ytterbium are eluted using a solution of a chelator at elevated temperature with the aid of a system consisting of at least two series connected columns of decreasing diameter, filled with a sulphonic cation resin. The separation of ytterbium and lutetium is carried out in the presence of a bivalent ion of a stable intercalator element selected from the group consisting of cobalt, lead or zinc, in an amount in mEq that is equal to not less than 80% of the total capacity of the last column in the direction of travel of the solution. A solution of ethylenediaminetetraacetic acid or nitrilotriacetic acid is used as the eluent.