Selective catalytic reduction with ammonia or a compound which can be decomposed to give ammonia is a known process for removing nitrogen oxides from the exhaust gas of predominantly lean-burn internal combustion engines. Most of the vanadium-containing SCR catalysts used for this purpose to date are notable for a good conversion profile. However, the volatility of vanadium oxide at relatively high exhaust gas temperatures can lead to the emission of toxic vanadium compounds. Zeolite-based SCR catalysts, which are used especially in batchwise SCR systems, are a very costly solution to the problem. A process is presented, with which a homogeneous cerium-zirconium mixed oxide is activated for the SCR reaction by introducing sulfur and/or transition metal in a defined manner. The use of this process provides a highly active, ageing-stable SCR catalyst which constitutes a vanadium-free, inexpensive and high-performance alternative to the SCR catalysts to date and is suitable especially for use in motor vehicles.