The aim of the study was to analyse the chemical composition and oxidation stability of selected cold-pressed oils and oil mixtures. The oils were tested for their initial quality, fatty acid composition, total phenolic compounds, DPPH, and ABTS free radical scavenging activity. The Rancimat method was used to assess oxidative stability. The obtained results were subjected to principal component analysis (PCA) to determine the influence of selected chemical properties on the oxidative stability of the oil. It has been found that different factors of oil quality influence the stability of cold-pressed oils. The highest correlation coefficient was noted between the induction time, peroxide value, and TOTOX indicator (r = 0.89). Fatty acid composition, including the percentage of SFA, MUFA, PUFA, and the ability to scavenge ABTS captions radicals, did not significantly affect the oxidative stability of the oils. Black cumin seed oil was the most resistant to the oxidation processes in the Rancimat apparatus, mainly due to the high content of phenolic compounds (384.66 mg GAE/100 g). On the other hand, linseed oil and its mixtures were the least stable. Their fatty acid composition was dominated by a polyunsaturated α-linolenic fatty acid, significantly reducing the antioxidant resistance.