A catalyst for purifying exhaust gases of a diesel engine. The catalyst contains two functional layers superimposed on an inert supporting body, whereby the first layer, which is situated directly on the supporting body, has a nitrogen oxide storage function and the second layer, which is in direct contact with the exhaust gas, has a catalytic function. The second functional layer additionally has a hydrocarbon-storage function and its catalytic function is provided by catalytically active noble metals of the platinum group which are deposited in highly dispersed form on finely divided, acidic carrier materials. Nitrogen oxides in the oxygen-rich exhaust gas of a diesel engine can be converted with optimal utilization of the reductive constituents contained in the exhaust gas. For this purpose, no reducing agents going beyond the reductive components (carbon monoxide and hydrocarbons) which are contained as a consequence of incomplete combustion need to be added to the exhaust gas. Nevertheless, rates of conversion in respect of the nitrogen oxides are obtained, averaged over practical driving cycles, which lie distinctly above the rates of conversion of conventional reduction catalysts.