A process for catalytic cracking of a hydrocarbon feed with a boiling point of higher than 350°C, using a fine control of the residual coke level on the regenerated catalyst, said process comprising at least one reaction zone for contacting the hydrocarbon feed to be treated and the catalyst in a transported bed, and a regeneration zone for said coked catalyst at the discharge from the reaction zone, said regeneration zone being divided into a first regeneration stage in a fluidised bed operating with partial combustion, that is to say with a shortage of air, generating a catalyst whose residual coke rate is between 0.3% and 0.7% and a second regeneration stage in a fluidised bed disposed in series in relation to the first stage and operating with total combustion, that is to say with an excess of air, and generating a catalyst whose residual coke rate is less than 0.15%, transfer of the catalyst from the first to the second stage being implemented by the transport line supplied by a gas flow and provided with a valve for controlling the catalyst flow placed at the base of the transport tube, the regenerated catalyst obtained following mixing of the partially regenerated and totally regenerated catalysts having a residual coke rate of higher than 0.15% and preferably higher than 0.25%, said coke rate being obtained by controlling the circulation of the totally regenerated catalyst which is obtained at the discharge from the second regeneration stage which is a) either passed back into the first regeneration stage by means of a transfer line, a fluidised chamber, a transport tube and a control valve, from which first stage the catalyst resulting from mixing of the two stages and having the desired coke level is passed back to the reaction zone by the conduit, b) or is passed into a dedicated mixing chamber by means of a transfer line, a fluidised chamber, a transport tube and a control valve, in which mixing chamber the totally regenerated catalyst is mixed with the partially regenerated catalyst issuing from the first regeneration stage, from which mixing chamber said catalyst resulting from the mixing operation and having the desired coke level is passed back into the reaction zone by the conduit, the process being characterised in that the catalyst issuing from the second regeneration stage operating with total combustion is passed back into the first regeneration stage operating with partial combustion or into the mixing chamber by means of an assembly of conduits comprising in the direction of flow of said catalyst: 1) the fluidised chamber operating at a fluidisation speed of between 0.05 m/s and 0.1 m/s, the catalyst flowing downwardly in said chamber at a speed of less than 0.5 m/s, 2) the transport tube operating at a catalyst transport speed of between 1 and 3 m/s, and 3) the control valve for controlling the flow of catalyst pilot-controlled by the level of catalyst in the second regeneration stage and which in case b) is disposed upstream of the mixing chamber. a) either passed back into the first regeneration stage by means of a transfer line, a fluidised chamber, a transport tube and a control valve, from which first stage the catalyst resulting from mixing of the two stages and having the desired coke level is passed back to the reaction zone by the conduit, b) or is passed into a dedicated mixing chamber by means of a transfer line, a fluidised chamber, a transport tube and a control valve, in which mixing chamber the totally regenerated catalyst is mixed with the partially regenerated catalyst issuing from the first regeneration stage, from which mixing chamber said catalyst resulting from the mixing operation and having the desired coke level is passed back into the reaction zone by the conduit, the process being characterised in that the catalyst issuing from the second regeneration stage operating with total combustion is passed back into the first regeneration stage operating with partial combustion or into the mixing chamber by means of an assembly of conduits comprising in the direction of flow of said catalyst: 1) the fluidised chamber operating at a fluidisation speed of between 0.05 m/s and 0.1 m/s, the catalyst flowing downwardly in said chamber at a speed of less than 0.5 m/s, 2) the transport tube operating at a catalyst transport speed of between 1 and 3 m/s, and 3) the control valve for controlling the flow of catalyst pilot-controlled by the level of catalyst in the second regeneration stage and which in case b) is disposed upstream of the mixing chamber. 1) the fluidised chamber operating at a fluidisation speed of between 0.05 m/s and 0.1 m/s, the catalyst flowing downwardly in said chamber at a speed of less than 0.5 m/s, 2) the transport tube operating at a catalyst transport speed of between 1 and 3 m/s, and 3) the control valve for controlling the flow of catalyst pilot-controlled by the level of catalyst in the second regeneration stage and which in case b) is disposed upstream of the mixing chamber.