I wanted to rotate the nut in the picture around its own z-axis. So I turned the transform orientations to Normal. But somehow the rotation of this object as well as of the two adjacent obejcts ehaves in a way I don't understand. When I move the object along its normals it behaves the way I would expect.
I also added a new object (the cube in the background) and tried to do the same with it which works well.
If this is of any help: I originaly rotated the object this way by snapping it to another face, afterwards made linked copies and used a mirror modifier. But I can't seem to get behind this issue.