An aftertreatment system for an internal combustion system includes an exhaust duct, an oxidation catalyst disposed in the exhaust duct and a particulate filter disposed in the exhaust duct downstream of the oxidation catalyst. The internal combustion engine is operated to perform a regeneration process of the particulate filter. A first value of exhaust gas temperature in the exhaust duct between the oxidation catalyst and the particulate filter is determined. A second value of exhaust gas temperature in the exhaust duct downstream of the particulate filter is determined. A malfunctioning of the oxidation catalyst is determined when the first value of exhaust gas temperature is below a first predetermined threshold value thereof and contemporaneously the second value of exhaust gas temperature is above a second predetermined threshold value thereof during the regeneration process.