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The comparative study of the mechanism of oxidation of 2,3,5,6-tetra-Me-pyrazine-di-N-oxide (Pyr2) as a mediator of electrocatalytic oxidation of methanol (MeOH) was carried out at glassy carbon (GC) and multi-walled carbon nanotube (MWCNT) paper electrodes in 0.1 M LiClO4 solutions in acetonitrile by the methods of cyclic voltammetry, EPR electrolysis, the dependence of the differential double layer capacitance of the electrode C on potential E, scanning electron microscopy (SEM) and high-resolution transmission electron microscopy (HR-TEM). It was found that the oxidation current of Pyr2 at MWCNT paper electrode (as in the case of SWCNT paper electrode found early) in the absence of MeOH exceeds by several times the oxidation current of the ferrocene reference. This effect is attributed to the adsorption of Pyr2 at the surface of these electrodes and the subsequent increase in the surface concentration of Pyr2 and the current of its oxidation. Catalytic currents were recorded during the oxidation of Pyr2 at GC and MWCNT paper electrodes in presence of MeOH. The effect of MeOH, acid and water on the shape of CVs and the intensity of EPR signal of Pyr2 radical cation was investigated. These results were explained by the E1C1E2C2 mechanism of two-stage electrode process characterized by catalytic current recorded at the second electrode stage. The overall two-electron catalytic oxidation of methanol in complex with the Pyr2 radical cation was assumed to occur. The catalytic efficiency of MeOH oxidation increases by 7 times at the use of MWCNT paper electrode instead of GC. The results pointed out that in process of electrocatalytic oxidation organic compounds in the presence of aromatic di-N-oxides as mediators the effect of the electrodes made of SWCNT paper (studied early) and MWCNT paper (studied in this paper) are similar.