A screw drive (10a) with rolling elements, optionally a ball screw drive, includes a screw spindle with a spindle axis (S) and a double nut (14a) running on the screw spindle, with two separately formed single nuts (16a , 18a) which are substantially rigidly joined in the direction of the axis (S) of the spindle. In order to set a desired play or bias relative to the screw spindle, the two single nuts (16a, 18a) can be turned continuously about the axis (S) of the spindle relative to each other and fixed in any relative rotary position corresponding to the desired play or bias. According to the invention, a first of the two single nuts or an intermediate element (28a) joined thereto and arranged between the two single nuts, as a first alternative, is welded to one of the two single nuts or to at least one part (42a) joined thereto or, as a second alternative, has at least one peripheral section pressed into an associated aperture in one of the single nuts.