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In the present work the ignition and quench phenomena of the combustion of a carbon surface in oxidizing cross flow is investigated theoretically. For certain values of moisture content and of heterogeneous reaction rates, multiple ignition and quench phenomena are observed together with non‐monotonous dependence of the burning rate upon the surface temperature. These phenomena occur in the region of transition from the reaction controlled to the transport controlled regime. In dependence upon reaction rates this regime extends from 1300 K to about 2000 K.