The 1,3-random-2-random theory was proposed several years ago to explain the fatty acid distribution in vegetable oil triacylglycerols. However, by demonstrating an asymmetry between positions sn-1 and sn-3 in olive oil, cocoa butter, sunflower oil, etc., a number of studies have shown that this theory does not hold true for some oils and fatty acids. Accordingly, the distribution of fatty acids in sunflower triacylglycerols has been studied, calculating the alpha coefficient of asymmetry in several combinations of standard linoleic, high-oleic, and high-stearic sunflower oils. The results obtained from the oils of these lines and from single seed oil samples indicate that the asymmetry for saturated fatty acids is greater in high-oleic than in standard linoleic backgrounds. Hence, the distribution of the fatty acids within the triacylglycerol molecule appears to depend not only on the fatty acid under study but also on the other fatty acids in the oil. Thus, it is demonstrated for the first time that certain fatty acids can influence the distribution of other fatty acids within triacylglycerols.