Abstract: Process for producing a steel strip or sheet, in which liquid steel is cast in a continuous-casting machine to form a thin plate and, while making use of the casting heat, is fed through a furnace device, is roughed in a roughing stand to a pass-over thickness and is rerolled in a finishing rolling stand to form a steel strip or sheet of the desired final thickness, in which (a) to produce a ferritically rolled steel strip, the strip, the plate or a part thereof is fed without interruption at least from the furnace device, at speeds which essentially correspond to the speed of entry into the roughing stand and the following reductions in thickness, from the roughing stand to a processing device which is disposed downstream of the finishing rolling stand, the strip coming out of the roughing stand being cooled to a temperature at which the steel has an essentially ferritic structure; (b) to produce an austenitically rolled steel strip, the strip coming out of the roughing roll is brought to or held at a temper