For producing synthesis gas, SG, from a hydrocarbon feed and optionally from recycled compounds, F, a first feed F1 supplemented with steam undergoes steam reforming in a multi-tube reactor-exchanger R comprising a plurality of reaction tubes (38) containing a steam reforming catalyst and a shell containing said tubes, to produce a first synthesis gas SG1; reaction tubes (38) are heated principally by convection by circulating a fluid HF in the shell external to said tubes, in which HF is a staged partial oxidation stream with oxygen of a second feed F2 at a pressure in the range 0.5 to 12 MPa, to produce a second synthesis gas SG2; and the synthesis gas SG is produced by mixing SG1 and SG2.