An oxygen absorbent composition at least comprising: a polyester oligomer containing a constitutional unit having at least one tetralin ring selected from the group consisting of constitutional units represented by the following formulas to, where R each independently represent a monovalent substituent, which is at least one selected from the group consisting of a halogen atom, an alkyl group, an alkenyl group, an alkynyl group, an aryl group, a heterocycle group, a cyano group, a hydroxy group, a carboxyl group, an ester group, an amido group, a nitro group, an alkoxy group, an aryloxy group, an acyl group, an amino group, a mercapto group, an alkylthio group, an arylthio group, a heterocyclic thio group and an imide group, and which may further have a substituent; where m each independently represent an integer of 0 to 3; where n each independently represent an integer of 0 to 6, at least one hydrogen atom is bound to the benzyl position of the tetralin ring; and where X each independently represent a divalent group containing at least one group selected from the group consisting of an aromatic hydrocarbon group, a saturated or unsaturated alicyclic hydrocarbon group, a straight or branched and saturated or unsaturated aliphatic hydrocarbon group and a heterocycle group; and a transition metal catalyst, wherein the transition metal catalyst is a catalyst comprising at least one transition metal selected from the group consisting of iron, cobalt, nickel and copper, and the transition metal catalyst is contained in an amount of 0.001 to 10 parts by mass in terms of a transition metal based on 100 parts by mass of the polyester oligomer, and wherein the polyester oligomer has a number average molecular weight of 500 to 10000, and the number average molecular weight is measured by Gel Permeation Chromatography-low-angle laser light scattering GPC-LALLS using a "HLC-8320GPC" measurement apparatus manufactured by Tosoh Corporation, wherein the molecular weight refers to a polystyrene equivalent value, and wherein the polyester oligomer is a polyester oligomer obtained by reacting a terminal stopping agent containing a monovalent aliphatic alcohol or a monovalent aliphatic organic acid with the oligomer. a polyester oligomer containing a constitutional unit having at least one tetralin ring selected from the group consisting of constitutional units represented by the following formulas to, where R each independently represent a monovalent substituent, which is at least one selected from the group consisting of a halogen atom, an alkyl group, an alkenyl group, an alkynyl group, an aryl group, a heterocycle group, a cyano group, a hydroxy group, a carboxyl group, an ester group, an amido group, a nitro group, an alkoxy group, an aryloxy group, an acyl group, an amino group, a mercapto group, an alkylthio group, an arylthio group, a heterocyclic thio group and an imide group, and which may further have a substituent; where m each independently represent an integer of 0 to 3; where n each independently represent an integer of 0 to 6, at least one hydrogen atom is bound to the benzyl position of the tetralin ring; and where X each independently represent a divalent group containing at least one group selected from the group consisting of an aromatic hydrocarbon group, a saturated or unsaturated alicyclic hydrocarbon group, a straight or branched and saturated or unsaturated aliphatic hydrocarbon group and a heterocycle group; and a transition metal catalyst, wherein the transition metal catalyst is a catalyst comprising at least one transition metal selected from the group consisting of iron, cobalt, nickel and copper, and the transition metal catalyst is contained in an amount of 0.001 to 10 parts by mass in terms of a transition metal based on 100 parts by mass of the polyester oligomer, and wherein the polyester oligomer has a number average molecular weight of 500 to 10000, and the number average molecular weight is measured by Gel Permeation Chromatography-low-angle laser light scattering GPC-LALLS using a "HLC-8320GPC" measurement apparatus manufactured by Tosoh Corporation, wherein the molecular weight refers to a polystyrene equivalent value, and wherein the polyester oligomer is a polyester oligomer obtained by reacting a terminal stopping agent containing a monovalent aliphatic alcohol or a monovalent aliphatic organic acid with the oligomer.