A process for producing hot-rolled steel strip from strip-form cast feedstock in consecutive work steps, in which the solidified feedstock is roughed down in a particular sequence by reversing roll passes. The feedstock is then coiled up for temporary storage in a furnace atmosphere, and finally supplied to a finishing train to be rolled down to the finished band thickness. The machine for carrying out this process includes a temperature-controlled intermediate storage furnace provided between a reversing Steckel mill and the multi-stand finishing train.