A method and a device for machining the tooth edges (23, 25) developed between each end face (22, 24) and the tooth flanks (26, 27) of end-cut work wheels (2). The axis of rotation (20) of the spindle that carries the machining tool (21) is displaced around an orthogonal swivel axis (16) relative to the tool axis of rotation so that the cutting directions are opposite to each other with respect to the work wheel (2) in the machining of the lower tooth edges (23) and the upper tooth edges (25).