The stabilization efficiency of flavonoids (rutin and hesperidin) in polyester (polylactide (PLA) and polyhydroxyalkaonate (PHA)) composites under oxygen at high temperature was investigated. The polymer was homogenized with three antioxidants then processed by extrusion. The effects of stabilizers on the following physicochemical properties were investigated: melt flow, Vicat softening temperature, surface energy, and color change (Cie-Lab space). The aim of this study was to improve the stability of aliphatic polyesters by extending and controlling their lifetime. Differential Scanning Calorimetry DSC and Thermogravimetric analysis DTG methods were used to confirm the stabilizing effects (the inhibition of oxidation) of flavonoids (rutin and hesperidin) on the ageing process of biodegradable polymers. The levels of migration of plant antioxidants from PLA and PHA were determined and compared to the industrial stabilizer (Chimassorb 944 UV absorber). Based on this study, a comparable-to-higher efficiency of the proposed flavonoids for the stabilization of polyesters was found when compared to the commercial stabilizers. Thus, in the future, natural plant-derived substances may replace toxic hindered amines, which are commonly used as light stabilizers (HALS-Hindered Amine Light Stabilizers) in the polymer industry.