Abstract: On a device for grinding the profile of a rotating workpiece (5), the rotating workpiece (5), arranged on a swivel table (6) for axial and transverse displacement with reference to the work spindle (4), is according to the invention positioned prior to grinding and relative to a swivel table axis (D) such that the radial centre of a circular arc shaped workpiece profile section (7) due for high precision grinding coincides with the swivel axis (D) of the swivel table (6). The thereby attained reduction of the number of simultaneous axes motions involved in grinding this profile section (7) to a single machine axis permits an optimum profile accuracy.