A method for operating a system for the steam reforming of a hydrocarbon or hydrocarbon derivative starting substance includes, during the cold-starting of the system, at least part of a reforming reactor is used as a multi-function reactor unit. A fuel and an oxygen-containing gas is delivered to the reforming reactor as a catalytic burner unit in a first operating phase. In a subsequent second operating phase, the reforming reactor is a partial oxidation unit for the starting substance. Water may be added shortly before the second operating phase commences. Alternatively, or in addition thereto, the fuel flow rate may be increased with a rising temperature in the first operating phase or a substoichiometric oxygen flow rate may be set as early as in the first operating phase.