The invention concerns a process for producing synthesis gas, SG, from hydrocarbons and/or recycled compounds. In the process: a stream comprising a first feed F1 supplemented with steam undergoes steam reforming in a multi-tube reactor-exchanger R having a shell and reaction tubes containing a steam reforming catalyst within the shell; the reaction tubes are heated by convection by circulating in the shell, in overall counter-current mode, a heating fluid HF external to the tubes, which fluid comprises a first combustion gas stream of a second feed F2, then fluid HF is mixed, in 1 to 4 complementary combustion zones internal to the shell, with a third feed F3 and a gas comprising oxygen, to increase the temperature of the HF, and then the mixture obtained circulates in R to heat the reaction tubes in a complementary manner; and SG is produced from the steam reforming effluent from F1 and optionally part or all of the HF.