Selective catalytic reduction with ammonia or a compound that decomposes to ammonia is a known method for the removal of nitrogen oxides from the exhaust gas of primarily lean-burn internal combustion engines. The vanadium-containing SCR catalysts that have long been generally used for this are characterized by a good conversion profile. However, the volatility of vanadium oxide can, at higher exhaust gas temperatures, lead to the emission of toxic vanadium compounds. Zeolite-based SCR catalysts, which are used in particular in discontinuous SCR systems, constitute a very cost-intensive solution for the problem.A method is proposed by which a homogeneous cerium-zirconium mixed oxide is activated for the SCR reaction in a defined manner by the introduction of sulphur and/or transition metal. Using this method, a highly active, ageing-resistant SCR catalyst is provided, which represents a vanadium-free, cost-effective and high-performance alternative to the existing SCR catalysts and is suitable in particular for use in motor vehicles.