The invention relates to a device (20) comprising a workpiece spindle (21) for receiving a gear wheel (25), a tool spindle (29) for receiving a tool and several drives (X, Y, Z, B, C, A1) for machining the gear wheel in individual divisions. According to the invention, one tooth gap of the gear wheel is machined and then the tool is displaced in relation to the gear wheel in order to remove the tool from the tooth gap. The gear wheel is then rotated by a division and the tool is placed against the wheel again to machine another tooth gap. One of the drives (C) can be controlled in such a way that the relative displacement involves a tilting displacement, which modifies the relative angle between the tool and the gear wheel, the tilting displacement being co-ordinated with the displacement of a division.