The invention relates to a system and a control method for an exhaust aftertreatment system (10) of an engine (12) in which one or more constituents of the exhaust gas are oxidized in an oxidation catalyst (20) and one or more constituents of the exhaust gas are deoxidized in a selective-catalytic-reduction catalyst (70), wherein the exhaust gas flows from the oxidation catalyst (20) to the selective-catalytic-reduction catalyst (70). It is. proposed to control the flow of the exhaust gas through the oxidation catalyst (20) depending on a desired ratio among the one or more constituents, wherein the exhaust gas enters the selective-catalytic-reduction catalyst (70) with the desired ratio among the one or more constituents; and to establish the desired ratio among the one or more constituents so that at a given reaction temperature in the selective-catalytic-reduction catalyst (70) one specific chemical reaction is selected out of a group of possible chemical reactions which can take place among the one or more constituents of the exhaust gas and the catalyst material in the selective-catalytic-reduction catalyst (70) at the given temperature, wherein the selected specific chemical reaction has a higher probability to be performed than each single one of the other chemical reactions which are not selected.