The thermochemical conversion of biomass in smouldering combustion is investigated here by combining experiments and modeling at two scales: matter (1 mg) and bench (100 g) scales. Emphasis is put on the effect of oxygen (0-33 vol.%) and oxidation reactions because these are poorly studied in the literature in comparison to pyrolysis. The results are obtained for peat as a representative biomass for which there is high-quality experimental data published previously. Three kinetic schemes are explored, including various steps of drying, pyrolysis and oxidation. The kinetic parameters are found using the Kissinger-Genetic Algorithm method, and then implemented in a one-dimensional model of heat and mass transfer. The predictions are validated with thermogravimetric and bench-scale experiments and then analyzed to unravel the role of heterogeneous reaction. This is the first time that the influence of oxygen on biomass smouldering is explained in terms of both chemistry and transport phenomena across scales. (C) 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).