A process for producing a hydrogen-containing product gas by catalytic steam-hydrocarbon reforming with an overall steam-to-carbon molar ratio between 1.5 and 2.4 for the process. The process stream is reacted in at least two prereformers prior to reaction in catalyst-containing tubes in a top-fired reformer furnace. The process stream is reacted adiabatically in the first prereformer, while the process stream is heated prior to being introduced into the second prereformer and/or the second prereformer is heated. The process avoids carbon formation on the catalyst in the catalyst-containing tubes in the primary reformer.