The adherence to future legally obligatory exhaust gas limit values for diesel vehicles in Europe, North America and Japan requires not only the removal of particles but also effective removal of nitrogen oxides from the exhaust gas (‘deNOx’). The ‘active SCR process’ is the preferred method for this. The nitrogen oxide conversions achieved by means of this process are particularly high when an optimal NO2/NOx ratio, preferably 0.5, is set upstream of the SCR catalyst. The invention proposes a process which solves the problem of supplying NO2 in accordance with requirements by means of temperature control of the precatalyst which is decoupled from the operating state of the engine. In an associated apparatus, a precatalyst (1) which contains at least one oxidation component and whose temperature can be controlled independently of the operating state of the engine and an active SCR stage comprising an SCR catalyst (3c) with upstream metering facility (3b) for a reducing agent from an external source (3a) are arranged in series. A particle filter (2) can be arranged between precatalyst and metering facility. The precatalyst preferably additionally contains a nitrogen oxide storage material.