The present invention relates to an exhaust system for an internal combustion engine, in particular in a motor vehicle, with an exhaust line in which an oxidation catalyst is provided for treatment of the exhaust gases coming from the internal combustion engine. To be able to heat the oxidation catalyst more rapidly in a cold start of the internal combustion engine, a pre-oxidation unit may be provided in the exhaust line upstream from the oxidation catalyst and connected to a secondary fuel supply and adapted so that it partially oxidizes the secondary fuel supplied in combination with an oxidizer in a catalyst heating operation and the partially oxidized intermediate products are supplied to the oxidation catalyst for complete oxidation.