A double-layer three-way catalyst for purification of the exhaust gases from internal combustion engines which has excellent activity and thermal stability is described. The catalyst contains active aluminum oxide and a first cerium/zirconium mixed oxide which are both catalytically activated with palladium in the first layer applied to a catalyst support. In the second layer which is in direct contact with the exhaust gas, the catalyst likewise contains an active aluminum oxide and a second cerium/zirconium mixed oxide which are both catalytically activated with rhodium. The second cerium/zirconium mixed oxide has a higher zirconium oxide content than the first mixed oxide.