Polymers tend to react with oxygen and therefore require stabilization for most applications. For that purpose polymer antioxidants are used to protect polymers from oxidation and degradation. However, antioxidants are known to migrate and diffuse out of polymer matrices and are physically lost. They can contaminate the surrounding of the polymer, for example drinking water in water pipeline systems. One approach to hinder antioxidant loss is to immobilize antioxidants on other additive molecules with reduced migration. Therefore, antioxidants are covalently linked to molecules with a high molecular weight which results in hindered migration. In this thesis two different nanomaterials - multi-walled carbon nanotubes (MWCNT) and cellulose nanocrystals (CNC) - are used as supporting materials because of their additional beneficial effects on polymeric materials. MWCNT are known to enhance mechanical, electrical, thermal, optical, and electrochemical properties of polymers in polymer-nanocomposites. Phenolic antioxidants were covalently grafted to MWCNT by amide bond formation on oxidized nanotubes. The degree of chemical functionalization was verified by thermogravimetric analysis and qualitative characterization was performed with FT-IR, raman spectroscopy, and NMR analysis. MWCNT-immobilized antioxidants were compounded with isotactic and amorphous polypropylene and their stabilization effect was tested by means of oxidation induction time measurements. It was found that the method of stabilizer addition strongly influences the dispersion of antioxidants within polymeric materials, which is discussed along with its impact on the stabilization effect. CNC are bio-based and non-toxic and improve mechanical, optical, and barrier properties of polymeric materials. Two different synthesis strategies for the chemical functionalization of CNC with antioxidant groups were performed. The first includes a carboxymethylation step followed by amide bond formation. The second was realized by an ester bond formation via an antioxidant acid chloride. To improve the dispersion of CNC immobilized antioxidants in non-polar polymeric matrices additional aliphatic groups were introduced. The products were qualitatively characterized by FT-IR, solid-state NMR, thermogravimetric analysis, and if possible X-ray diffraction. The degree of functionalization was verified by quantitative titrations and the stabilization effect was determined by oxidation induction time measurements in squalane. The resulting MWCNT- and CNC-immobilized antioxidants possess a stabilizing effect which is influenced by several parameters. Beside the structure of the antioxidant itself, a homogeneous dispersion and its solubility within the polymer matrix are important.