The so-called ‗SPLET‘ mechanisms of reaction of dihydroxyfumaric acid (DHFA) with the Stable Radical DPPH• has an ionic character and includes the formation of the charge-transfer complex as the main stage, which is formed from the protonated DPPH• molecule and the anion of DHFA arising due to their electrolytic dissociation in the water-methanol medium [1]. In its turn, it was found by us (by the usage of the program GAUSSIAN09 [2]) that the radical (HAT) mechanism is being realized in the three stages shown below: Step I: Direct transfer of the hydrogen atom from the –OH group of DHFA to the functional group –N•-N = of the DPPH radical. As the result, the radical of DHFA• is obtained, which is a monodehydrogenated form of DHFA. Step II: Transfer of the second hydrogen atom from the hydroxyl group of the above formed radical DHFA• to the nitro group of the second DPPH• radical. Step III: intramolecular hydrogen atom transfer from the nitro-NO2 group to the –N-N= functional group of DPPH resulting in two neutral molecules DPPH and one molecule of dioxosuccinic acid – DOSA.