Abstract: A process for grinding a cylindrical journal is provided, in which the workpiece is rotationally drivably received and held in a work spindle. The grinding disk, which is cylindrically trimmed on its outer circumference, is brought into engagement with the journal to be ground. In order to be able to avoid twist structures during the cylindrical grinding, or at least to keep them within tolerable limits, while approaching the desired circumferential speed of the grinding disk and that of the workpiece within a respectively permissible spread, the rotational disk speed under a load during the grinding and/or the rotational workpiece speed under a load is/are continuously changed during each grinding operation and/or adjusted such that the ratio of the rotational disk speed to the rotational workpiece speed is disharmonic to as high a degree as possible; that is, that integral or simple fractional ratios of the disk rotational speed to the workpiece rotational speed are avoided.