Reducing the saturated fatty acid content of sunflower (Helianthus annuus L.) oil would benefit the sunflower industry through increased consumer preference for a low saturated sunflower product. This study was conducted to determine the inheritance of low stearic and low palmitic acid content found in three sunflower mutant lines treated with two mutagens, N‐nitroso‐N‐methylurea (NMU) and ethyl methanesulfonate (EMS) at rates of 1 and 2 g kg−1. The fatty acid content of approximately 6800 M5 lines was analyzed by gas chromatography. Two M5 lines, HA 821 LS‐1 and RHA 274 LS‐2, had lower stearic acid content (41 and 20 g kg−1), and one M5 line, RHA 274 LP‐1, had lower palmitic acid content (47 g kg−1) than their respective parental lines. Segregation ratios of F2 and testcross progeny indicated that the low stearic acid content in HA 821 LS‐1 was controlled by one gene, designated fas1, with additive gene action. The low stearic acid content in RHA 274 LS‐2 was controlled by two genes with additive gene action. The first gene was designated fas2, and the second gene was temporarily designated fasx. The allele fap1 was identified in RHA 274 LP‐1 to control low palmitic acid content with additive gene action. The combination of the alleles for low stearic and low palmitic acid content identified in this study could reduce the total saturated fatty acid content of oil in sunflower from 130 g kg−1 to less than 80 g kg−1.