The invention provides a multistep process for preparing a low-sulfur reformate gas for use in a fuel cell system. The process comprises catalytic steam reforming of a reactant gas mixture comprising sulfur-containing hydrocarbons and steam in a first step to make a reformate, reducing the carbon monoxide content of the reformate in a second step, passing the reformate over a sulfur absorber either directly after the first step or after passage through the second step, and desorbing the sulfur components optionally absorbed on the catalysts in the reforming and reducing process steps by periodically raising the temperature so as to cause the sulfer components to pass to the absorber, wherein the temperature of the absorber during operation of the process is always kept within a temperature interval which is an optimum for the absorber.