Antioxidant capacity of N-(1-naphthyl)valerohydroxamic acid (NVHA) and N-(1-naphthyl)phenylacetohydroxamic acid (NPAHA) has been evaluated by a novel approach employing the fluorescence microscopic single molecule observation method. This method allows direct observation of the changes in single DNA molecules. The DNA cleavage protection activity of the compounds was also assessed by the gel electrophoresis method. The applied methods confirmed that both compounds are capable of inhibiting the free radical mediated DNA damage. Free radical scavenging activity was assessed via the 2,2′-diphenyl-1-picrylhydrazyl free radical (DPPH) and lipid peroxidation inhibition methods. The effective concentration causing a 50 % inhibition of the DPPH concentration, EC50, was found to be 371.54 mM for NVHA and 365.95 mM for NPAHA. Its lipid peroxidation inhibition ability was calculated to be 40.91 % at 371.54 mM for NVHA and 41.14 % at 365.95 mM for NPAHA. These results show the antioxidant potential of the naphthyl hydroxamic acids.