Process including use of an arrangement for the gasification of fuels with oxygen or oxygen-containing gases and steam, includes a shaft-like vessel for receiving solid charging stock. A gas discharge duct is provided on the upper end of the vessel and a primary gas chamber is in connection with the shaft-like vessel on its lower end via a passage. In the primary gas chamber a burner is provided, which includes feedings for oxygen or oxygen-containing gases as well as for fuels. A trough for receiving slag is arranged below the primary gas chamber and a supporting bottoms is provided between the trough and the shaft-like vessel, reaching into the primary gas chamber, for the formation of a dumping material bed of the solid charging stock facing the burner by one dumping surface. In order to be able to gasify low-quality fuels into a high-quality product gas, the primary gas chamber includes a charging opening for charging a charging stock to be gasified. The supporting floor, on the side of the burner, is extended to such an extent that a second dumping stock bed of the charging stock to be gasified forms, lying in front of the first dumping surface and facing the burner with a second, free, dumping surface.