Volatile compounds formed in the course of the thermal decomposition of hydroperoxides during storage of sunflower oil were analyzed by headspace solid-phase microextraction sampling followed by gas chromatographic separation and mass spectral detection. The determining role of alkoxyl radicals in the process has been proven by electron spin resonance spectroscopic measurements. On the basis of analytical results, the reaction networks and mechanisms were constructed by computer modeling to describe the formation of volatile products of radical decomposition of hydroperoxides. We established that off-flavor aliphatic aldehydes are originated from only the alkoxyl radicals derived from trigliceride of linoleic acid. To find a specific additive, which redirects the formation of these radicals toward production of more stable species, is suggested.