A system and a method are provided for operating an exhaust aftertreatment system of an engine in which one or more constituents of the exhaust gas are oxidized in an oxidation catalyst and one or more constituents of the exhaust gas are deoxidized by means of a group of possible chemical reactions of different type between the one or more constituents of the exhaust gas and catalytic material arranged in a selective-catalytic-reduction catalyst, wherein the exhaust gas flows from the oxidation catalyst to the selective-catalytic-reduction catalyst, wherein the steps are performed: (a) adjusting at least one desired ratio among one or more pairs of the one or more constituents by varying a space velocity of the exhaust gas in at least the oxidation catalyst; (b) varying the space velocity of the exhaust gas by varying one or more operation parameters of the engine; and (c) establishing the ratio to a value at least approaching the desired ratio among the one or more pairs of the one or more constituents at the inlet of the selective-catalytic-reduction catalyst.