Theoretical kinetic studies of the reactions of several primarily alcohols with molecular oxygen are reported. Previously, by using Density Functional Theory (DFT) calculations, the hypothesis according to which the cetane number of a pure organic depends on the initiation rate of its homogeneous gas-phase reaction with molecular oxygen, was confirmed [See H. Abou-Rachid, L. Bonneviot, G. Xu, S. Kaliaguine, J. Mol. Struct. Theochem 621 (2003) 293]. A fair correlation was indeed obtained between the rate constant of the initiation step in the auto-ignition reaction and the value of the cetane number of the pure compound. In the present work, new kinetic calculations are reported for the series of primary alcohols: methanol, ethanol, propanol, butanol and pentanol. The DFT method appears to be satisfactory since the calculated rate constants are well correlated with both the experimental cetane number data, and the length of the (C+O) atom chain of these alcohols.