The invention relates to a method of and an apparatus for fluidised bed regeneration of a catalyst containing coke.The catalyst and some of the regeneration fumes are drawn off from the dense bed of a regenerator (1) and are introduced by gravity into an external exchanger at a junction point below the level of the dense bed of the regenerator. Heat exchange is carried out in the lower part of the exchanger (7) below the junction point. From the bottom end of the exchanger up to above the junction point a dense bed zone is created the level of which is established substantially at the height of the dense bed in the regenerator and a zone (15) of suitable size for the escape of regeneration gases and fluidisation gas. The gases and fumes are drawn off into the dilute fluidised phase (18) of the regenerator through a duct (17) while the catalyst is recycled to the dense bed of the regenerator through a different duct (25) from that in which the fluidisation air is circulating.Application to the regeneration of fluid bed cracking catalysts.