Oxygen radical formation in mitochondria is a highly important, but incompletely understood, attribute of eukaryotic cells. I propose a kinetic model in which the ratio between electrons entering the respiratory chain via FADH2 or NADH is a major determinant in radical formation. During the breakdown of glucose, this ratio is low; during fatty acid breakdown, this ratio is much higher. The longer the fatty acid, the higher the ratio and the higher the level of radical formation. This means that very long chain fatty acids should be broken down without generation of FADH2 for mitochondria. This is accomplished in peroxisomes, thus explaining their role and evolution. The model explains many recent observations regarding radical formation by the respiratory chain. It also sheds light on the reasons for the lack of neuronal fatty acid (beta-) oxidation and for beneficial aspects of unsaturated fatty acids. Last but not least, it has very important implications for all models describing eukaryotic origins.