The continuous refining of molten metal is carried out in a refining apparatus having communicating first and second refining stage spaces. Refining gas, such as oxygen, is blown into the molten metal in the presence of a slag layer on the molten metal. The molten metal and the slag are conveyed as two separate non-intermingled streams through the refining stage spaces, as distinguished from a slag-metal emulsion. The slag in the second refining stage space is caused continuously to flow back into the first refining stage space to form a slag layer on the molten metal in the first refining stage space. Refining gas is blown into the molten metal in the first refining stage space below the slag layer, and the molten metal is conveyed from the first refining stage space to the second refining stage space while preventing the flow of slag from the first refining stage space to the second refining stage space. Refining gas is blown onto the molten metal in the second refining stage space in the presence of slag so that a slag layer on the molten metal in the second refining stage space is formed. The molten metal and the slag are separated from each other after the molten metal has passed through the second refining stage space.