Poland is one of the largest producers of hazelnuts in Europe; however, information regarding the storage of cold-pressed hazelnut oil is limited. Thus, the aim of this study was to determine the oxidative indices and fatty acid composition of oils from six hazelnut cultivars during 9 months of storage. At the beginning of storage, the hazelnut oils showed zero or very low oxidation values, which indicated the absence of initial triglyceride hydrolysis and fatty acid oxidation. Acid values increased with storage time, which was statistically significant, ranging from 0.17 to 0.34 mg KOH/g oil. The peroxide value in the first 5 months of storage was undetectable, whereas after 9 months the oils showed a slight increase in oils obtained from the ‘Olbrzym z Halle’ cultivar, followed by the ‘Barcelonski’ cultivar, at 3.39 and 2.15 meq O2/kg, respectively. The lipid content of the kernels was very stable under storage conditions. Total monounsaturated fatty acid content exhibited the highest proportion, while saturated fatty acids (SFAs) had the lowest content over the entire storage period. The percentage of polyunsaturated fatty acids showed a small decrease during storage, but was not statistically significant; therefore, polyunsaturated fatty acid remained stable. The percentage of monounsaturated fatty acids decreased by approx. 1.6%, thus the percentage of SFA increased by approx. 13.7% during 9 months of storage. The oil yield ranged from 69% for nuts from the ‘Nottinghsamski’ cultivar to 75% from the ‘Webba Cenny’ and ‘Barcelonski’ cultivars.