The ball screw mechanism has spindle nut (1) arranged rotatably on a ball-rolling spindle (2) and between which balls (3) roll on ball grooves (4, 5). A driving wheel (20, 26) is fixed to the spindle nut (1), for driving the spindle nut. (1)The spindle nut (1) is mounted on a housing (8) by a rolling bearing (7). The bearing has an outer ring (9, 23) fixed to the housing (8) the outer ring (9, 23) has a ring (15, 29) surrounding the spindle nut (1), and a bearing running surface (10, 11) formed on the inner circumference of said the ring A radial flange (16, 28), adjoining the ring (15, 29), is fixed to the housing (8).