A method of producing a stabilized polymer, said method comprising the step of adding an antioxidant having a melting point of 70°C or lower to a catalyst system or a polymerization system before or during polymerization of a monomer having an ethylenically unsaturated bond wherein 0.005 to 0.5 parts by mass of said antioxidant is incorporated with respect to 100 parts by mass of a polymer obtainable by said polymerization of said monomer having an ethylenically unsaturated bond, wherein said antioxidant having a melting point of 70°C or lower contains at least one compound represented by the following Formula or: (wherein, R 1 and R 2 each independently represent any of an alkyl group having 1 to 40 carbon atoms, an aryl group having 6 to 40 carbon atoms, an arylalkyl group having 7 to 40 carbon atoms, a heterocycle-containing group having 3 to 25 carbon atoms and a combination thereof, which R 1 and R 2 are optionally bound together to form 5,5-dialkyl-1,3,2-dioxaphosphorinane; R 3 represents a direct bond, an alkylidene group having 1 to 40 carbon atoms or an arylene group having 6 to 40 carbon atoms; b represents an integer of 1 to 4; when b is 1, T represents a hydrogen atom, an alkyl group having 1 to 40 carbon atoms or an aryl group having 6 to 40 carbon atoms; when b is 2, T represents an alkylidene group having 1 to 40 carbon atoms, an arylene group having 6 to 40 carbon atoms or -O-; when b is 3, T represents an alkanetriyl group having 1 to 40 carbon atoms; when b is 4, T represents an alkanetetrayl group having 1 to 40 carbon atoms; a methylene group in said alkyl group, said alkylidene group, said alkanetriyl group and said alkanetetrayl group are optionally substituted with >C=O, -O-, -S-, -CO-O-, -O-CO-, -O-CO-O-, -NR 4 -, a phosphine, a phosphinite, a phosphonite, a phosphite, a phosphorane, a phosphonate or a combination thereof and also branched; and R 4 represents a hydrogen atom or an alkyl group having 1 to 4 carbon atoms); or (wherein, R 5 and R 6 each independently represent an alkyl group having 1 to 40 carbon atoms or an aryl group having 6 to 40 carbon atoms). (wherein, R 1 and R 2 each independently represent any of an alkyl group having 1 to 40 carbon atoms, an aryl group having 6 to 40 carbon atoms, an arylalkyl group having 7 to 40 carbon atoms, a heterocycle-containing group having 3 to 25 carbon atoms and a combination thereof, which R 1 and R 2 are optionally bound together to form 5,5-dialkyl-1,3,2-dioxaphosphorinane; R 3 represents a direct bond, an alkylidene group having 1 to 40 carbon atoms or an arylene group having 6 to 40 carbon atoms; b represents an integer of 1 to 4; when b is 1, T represents a hydrogen atom, an alkyl group having 1 to 40 carbon atoms or an aryl group having 6 to 40 carbon atoms; when b is 2, T represents an alkylidene group having 1 to 40 carbon atoms, an arylene group having 6 to 40 carbon atoms or -O-; when b is 3, T represents an alkanetriyl group having 1 to 40 carbon atoms; when b is 4, T represents an alkanetetrayl group having 1 to 40 carbon atoms; a methylene group in said alkyl group, said alkylidene group, said alkanetriyl group and said alkanetetrayl group are optionally substituted with >C=O, -O-, -S-, -CO-O-, -O-CO-, -O-CO-O-, -NR 4 -, a phosphine, a phosphinite, a phosphonite, a phosphite, a phosphorane, a phosphonate or a combination thereof and also branched; and R 4 represents a hydrogen atom or an alkyl group having 1 to 4 carbon atoms); or (wherein, R 5 and R 6 each independently represent an alkyl group having 1 to 40 carbon atoms or an aryl group having 6 to 40 carbon atoms).