Abstract: A bore machine for producing a very precise bore, as well as a method of producing a very precise bore in a workpiece. The bore machine has a main drive that drives the spindle rotationally as well as travel along the axial direction and an auxiliary drive that provides an oscillating motion in the axial direction that is overlayed over the forward travel motion of the spindle. The auxiliary drive has a first element with a wave-shaped surface and that is movable relative to a second element. During relative motion between the first and second elements, one element is forced to follow the peaks and valleys of the wave-shaped surface, thereby generating the oscillating motion. The auxiliary drive is driven such, that the relative motion between the two elements is at most 30% of the rotational speed of the spindle.