In this study ozone and the H2O2/O3 oxidation system are used to decolorize aqueous solutions of Orange II (Or-II) and Acid Red 27 (AR-27). Investigations are carried out in a semi-batch bubble column reactor. A system of series-parallel reactions is proposed to describe the mechanism of dye oxidation. The stoichiometric ratio for the first reaction is found to be 1 mol dye per mol O3, while the overall ozone demand for both reactions one and two is found to be 5 and 6 moles for Or-II and AR-27 respectively. Molecular and radical kinetics are compared: a radical scavenger, t-butanol, can be added to ensure only the molecular reaction of ozone, or hydrogen peroxide can be supplied through a peristaltic pump, to initiate radical reactivity. Results reveal that colour removal is ensured by direct ozone attack. For both dyes, TOC removal efficiencies of 50 - 60 % are obtained by the action of the hydroxyl free radical. However, this is not improved by addition of H2O2, thus demonstrating that organic species alone ensure HO degrees radical production during ozonation. Both the mass transfer and the ozone reactivity with the dyes are considered to evaluate the kinetic parameters for the molecular pathway.