A method is provided for producing a 0.8-4.5 mm thick steel strip with an amorphous, partially amorphous or fine-crystalline microstructure with grain sizes in the range of 10-10000 nm and also a flat steel product made therefrom. A molten steel is cast into a cast strip in a casting device and cooled down at an accelerated rate. Along with Fe and impurities that are unavoidable for production-related reasons, the molten material contains at least two elements belonging to the group “Si, B, C and P”. In this case, the following applies for the contents of these elements (in % by weight) Si: 1.2-7.0%, B: 0.4-4.0%, C: 0.5-4.0%, P: 1.5-8.0%. With a corresponding composition and a microstructure with corresponding characteristics, a flat steel product according to the invention has a HV0.5 hardness of 760-900.