A method is disclosed for continuously or semi-continuously producing hot steel strip which, starting from a slab guided through a slab-guiding device, is rolled in, for example, an at least four-stand roughing train to form an intermediate strip and, in a further sequence in a finish rolling train, into a final strip. The thickness of a slab cast in a die is reduced in the liquid core reduction process by means of the adjoining slab-guiding device to between 85 and 120 mm, a slab support length measured between the meniscus, i.e., the bath level, of the die and an end of the slab-guiding device facing the roughing train being at least 18.5 m, a casting speed ranging from 3.8 to 7 m/min, and slabs of different thicknesses being cast as a function of given casting speeds. Using the disclosed casting parameters, high-quality finishing may be provided with high production capacities.