In a method and apparatus for the continuous casting of preliminary steel sections, the liquid or molten steel is introduced substantially vertically into an open-ended die. The cross section of the cavity of the die is made up of a web part and one or more flange parts, for example, such as in preliminary double-T sections. The liquid core of the strand of the preliminary section is set in agitating motions transversely to the direction of continuous casting by selectively using electromagnetically-induced forces in the regions of the flange parts and/or of the web part. The agitating motions have the effect of exchanging the liquid steel in the molten crater of the strand of the preliminary section in and between flange parts and the web part. This allows the flow and temperature conditions in the liquid steel crater within the strand of the preliminary section to be actively influenced in a targeted manner and stabilization of the region of the surface of the liquid metal to be brought about, along with favorable and controllable flow conditions.