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PROBLEM TO BE SOLVED : To provide a polymer composition having improved cold-flow resistance that is produced at a low cost without a denaturation step. SOLUTION : In a method for producing a polymer composition, there are used a first constituent which is a rare-earth element compound or a rare-earth element compound containing a reactant of the rare-earth element compound and a Lewis base, a second constituent containing a compound represented by general formula (X), and a third constituent containing silica of a moisture content of 0.1 wt.% or higher. The method is characterized by including a step for mixing and aging the second constituent and the third constituent followed by addition of the first constituent for reaction, and then adding a monomer to produce a polymer; and dispersing the silica derived from the third constituent into the polymer, wherein the content of the silica in the polymer is higher than 0 pt.wt. and 5 pts.wt. or lower relatively to 100 pts.wt. of the polymer. COPYRIGHT : (C)2014, JPO&INPIT