The present invention relates to a mixed oxide of aluminium, of zirconium, of cerium, of lanthanum and optionally of at least one rare-earth metal other than cerium and lanthanum that makes it possible to prepare a catalyst that retains, after severe ageing, a good thermal stability and a good catalytic activity. The invention also relates to the process for preparing this mixed oxide and also to a process for treating exhaust gases from internal combustion engines using a catalyst prepared from this mixed oxide.