Thermoxidative stability was evaluated in triaclyglycerols (TAG) from the oils of the mutant sunflower lines CAS-3, CAS-4, and CAS-8 (with a high percentage of stearic acid), CAS-5 (with a high percentage of palmitic acid), all from standard highlinoleic genetic backgrounds, and the mutant sunflower line CAS-12 (with a high percentage of palmitic acid), from a high-oleic genetic background. These oils contained unusually high contents of TAG molecular species with one or two saturated fatty acids at the sn-1,3 positions. Purified total TAG devoid of tocopherols were subjected to controlled thermoxidative treatment at 180°C. Polymerized TAG were determined at 2-h intervals for 10 h. After this time, total polar compounds, oxidized TAG monomers, TAG dimers, and TAG oligomers were determined. TAG from highly saturated sunflower oils with levels of linoleic acid similar to those found in conventional sunflower oils (40–50%) showed enhanced thermal stability. In these TAG, the amount of polar compounds formed during the thermoxidative treatment was similar to that formed in the high oleic acid line. Excellent results were obtained for the TAG of the CAS-12 oil, which had the highest thermal stability, producing half the amount of polar compounds as the conventional line and less than two-thirds that of the high-oleic line.