These mutants display high levels of saturated fatty acids and therefore have oils with different physical properties, having a high potential for industrial applications [17,18]. The compositions of some of them are shown in Table 1, where typical compositions of high stearic and high palmitic sunflower mutants are shown. In a high linoleic background these oils can reach as much as 30% of either stearic or palmitic acids which, importantly, increases the solid fat content of such oils in a range of temperatures from 5 to 20 °C. In this regard, there is a deficiency of hard stock fats in the world because most currently-used vegetable oils are liquid. Solid fats are necessary for many industrial formulations including margarines, shortenings, fillings or confectionary [19]. These fats can be prepared from vegetable oils by hardening through hydrogenation. However, this process causes the production of unhealthy trans-fatty acids as a by-product [20]. The other alternative is based on the use of palm oil. Palm oil is rich in palmitate and has been extensively used for human nutrition. It is also a very productive crop [19,21]. However, the increased cultivation of palm trees in Indonesia is causing destruction of broad areas of tropical forest (accompanied by smoke pollution) giving ecological concerns to the production of these fats. There is some controversy as to whether high dietary palmitic acid can have an effect on plasma lipoproteins. However, no such potentially negative effects have been attributed to stearic acid. Thus, fats enriched in stearic acid, like high stearic sunflower, seem to be a promising alternative for a sustainable and ‘healthy’ source of solid fats. However, the original high stearic sunflower lines also contain high levels of linoleic acid, which diminishes