A steam/hydrocarbon reformer employing a conventional radiantly heated first reformer section and a flue-gas heated second reformer section is disclosed. The second reformer section comprises catalyst-containing tubes for partially reforming a hydrocarbon stream. The catalyst-containing tubes in the second reformer section are disposed in a conduit for conveying flue gas from the first reformer section, thereby receiving heat from the flue gases. The flue gases flow either cocurrent or countercurrent to the process gas in the catalyst-containing tubes in the second reformer section. The partially reformed hydrocarbon stream from the second reformer section is fed to the catalyst-containing tubes in the first reformer section thereby producing a hydrogen-rich synthesis gas.